Partial Fraction Decomposition (Linear Denominators)

Key Questions

• What does partial-fraction decomposition mean?

  Answer:

  Transforming a rational polynomial into a sum of simpler rational polynomials due to the factorization of the denominator.

  Explanation:

  Let me try and explain this to you. :)

  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  What is a partial-fraction decomposition?

  We are all familiar with the process of adding and subtracting fractions, e.g.

  #1/(x+1) + 2/(x+3) = (x+3)/((x+1)(x+3)) + (2(x+1))/((x+1)(x+3)) = (3x + 5)/(x^2 + 4x + 3)#

  Now, partial-fraction decomposition does exactly the reverse thing.

  It takes a rational polynomial, so a fraction like

  #(3x + 5)/(x^2 + 4x + 3)#

  from my example, and tries to decompose it into a sum of "simpler" fractions (to be more precise: into a sum of fractions which denominators are factors of the original fractions's denominator.)

  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  How to compute a partial-fraction decomposition?

  1) Linear and unique factors

  Let's stick with my example:

  #(3x + 5)/(x^2 + 4x + 3)#

  The first thing to do is a always to find a complete factorization of the denominator:

  #x^2 + 4x + 3 = (x + 3)(x + 1)#

  Here, all the factors are linear and unique, this is the simple case.

  The goal is to to find #A#, #B# so that the following equation holds:

  #(3x + 5)/((x+3)(x+1)) = A/(x+3) + B / (x+1)#

  To do so, first we should multiply both sides with the denominator:

  #<=> 3x+ 5 = A ( x+1) + B ( x+3)#

  Now, in order to solve this equation, we need to "group" the #color(red)(x)# terms and the terms #color(blue)("without "x)# (more precisely: #x^0# terms):

  #color(red)(3x)+ color(blue)(5) = color(red)(A * x) + color(blue)(A) + color(red)(B * x) + color(blue)(3 B)#

  Thus, we can form an equation based on the "red" terms and an equation based on the "blue" terms:

  #{ (3 = A + B), (5 = A + 3B):}#

  The solution of this linear equation system is inded #A = 2# and #B = 1# which leads us to the following partial-fraction decomposition:

  #(3x + 5)/((x+3)(x+1)) = A/(x+3) + B / (x+1) = 2/(x+3) + 1/(x+1)#

  ++++++++++++++++++++++

  2) Non-unique factors

  The computation is more complicated in case that the complete factorization of the original denominator doesn't consist just of linear and unique factors.

  Just a short example:

  Let's say we could factorize our rational polynomial like follows:

  #x/(x^2(x+1)^2(x-1)#

  As the factors #x# and #x+1# occur twice in the denominator, we need to account for that by building fractions with increasing powers of those factors.
  In this case, we would need to find #A#, #B#, #C#, #D# and #E# so that

  #x/(x^2(x+1)^2(x-1)) = A/x + B/x^2 + C/(x+1) + D/(x+1)^2 + E/(x-1)#

  holds.

  ++++++++++++++++++++++

  3) Non-linear factors

  Last but not least, there might be non-linear factors in your factorized denominator.

  Example:

  #1/(x^3+x) = 1/(x(x^2+1))#

  Unfortunately, you can't factorize #x^2+1# further (at least, for real numbers).

  In this case, your partial-fraction decomposition needs to look like follows:
  Find #A#, #B#, #C# so that the following equation holds:

  #1/(x(x^2+1)) = A/x + (Bx+C)/(x^2+1)#

  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When can a partial-fraction decomposition be useful?

  Finally, I'd like to note that a very common application of this method is integration of rational polynomials:

  If you need to compute

  #int (3x + 5)/(x^2 + 4x + 3) "d"x#

  and know that #1/(x+1) + 2/(x+3) = (3x + 5)/(x^2 + 4x + 3)# holds,

  it's easy to integrate by "splitting" the original fraction into a sum of simpler fractions and integrating each one of them:

  #int (3x + 5)/(x^2 + 4x + 3) "d"x = int 1/(x+1) "d"x + int 2/(x+3) "d"x#

  Lotusbluete · 2 · Nov 11 2015

• What does partial-fraction decomposition mean?
• What is the partial-fraction decomposition of #(5x+7)/(x^2+4x-5)#?
• What is the partial-fraction decomposition of #(x+11)/((x+3)(x-5))#?
• What is the partial-fraction decomposition of #(x^2+2x+7)/(x(x-1)^2)#?
• How do you write #2/(x^3-x^2) # as a partial fraction decomposition?
• How do you write #x^4/(x-1)^3# as a partial fraction decomposition?
• How do you write #(3x)/((x + 2)(x - 1))# as a partial fraction decomposition?
• How do you write the partial fraction decomposition of the rational expression #x^2/ (x^2+x+4)#?
• How do you write the partial fraction decomposition of the rational expression # (3x^2 + 12x - 20)/(x^4 - 8x^2 + 16)#?
• How do you write the partial fraction decomposition of the rational expression # 1/((x+6)(x^2+3))#?
• How do you write the partial fraction decomposition of the rational expression # (x^3-x^2+1) / (x^4-x^3)#?
• How do you write the partial fraction decomposition of the rational expression # (2x^2-18x-12)/(x^3-4x)#?
• How do you write the partial fraction decomposition of the rational expression # (x^4+1)/(x^5+6 x^3)#?
• How do you write the partial fraction decomposition of the rational expression # 6/(x^2-25)^2#?
• How do you write the partial fraction decomposition of the rational expression # (x^2+9)/(x^4-2x^2-8)#?
• How do you write the partial fraction decomposition of the rational expression # (9x^2 + 1)/(x^2(x − 2)^2)#?
• How do you write the partial fraction decomposition of the rational expression # 2 / (x(4x-1))#?
• How do you write the partial fraction decomposition of the rational expression # (5x^2 - 25x + 28) / (x^2(x-7))#?
• How do you write the partial fraction decomposition of the rational expression # (y^2 + 1) / (y^3 - 1)#?
• How do you write the partial fraction decomposition of the rational expression # (6x)/(x^3-8)#?
• How do you write the partial fraction decomposition of the rational expression # (x^4+6)/(x^5+7x^3)#?
• How do you write the partial fraction decomposition of the rational expression # 5/(x^2-1)^2#?
• How do you write the partial fraction decomposition of the rational expression # ( x-2 ) / (x^2 + 4x + 3)#?
• How do you write the partial fraction decomposition of the rational expression #(6x+5) / (x+2) ^4#?
• How do you write the partial fraction decomposition of the rational expression # (x-1)/(x^3 +x)#?
• How do you write the partial fraction decomposition of the rational expression # (2x-2)/((x-5)(x-3))#?
• How do you write the partial fraction decomposition of the rational expression # x/((x+7)(x+8)(x+9))#?
• How do you write the partial fraction decomposition of the rational expression # (x^2 -111)/ (x^4- x^2- 72)#?
• How do you write the partial fraction decomposition of the rational expression # 1 / ((x^2 + 1) (x^2 +4))#?
• How do you write the partial fraction decomposition of the rational expression #(x-5)/(x-2)^2#?
• How do you write the partial fraction decomposition of the rational expression #(2x-3) / (x-1)^2#?
• How do you write the partial fraction decomposition of the rational expression #1/(x^3-5x^2)#?
• How do you write the partial fraction decomposition of the rational expression #(x^2 + 1)/(x(x + 1)(x^2 + 2))#?
• How do you write the partial fraction decomposition of the rational expression #x^3/[x(x^2+2x+1)]#?
• How do you write the partial fraction decomposition of the rational expression #(x² + 2x-7) /( (x+3)(x-1)²)#?
• How do you write the partial fraction decomposition of the rational expression #z/(z^4-1) #?
• How do you write the partial fraction decomposition of the rational expression #(7x-2)/((x-3)^2(x+1))#?
• How do you write the partial fraction decomposition of the rational expression #(-3x^2 +3x - 5) / (3x^3 +x^2 + 6x +2)#?
• How do you write the partial fraction decomposition of the rational expression #x^2/(x+1)^3#?
• How do you write the partial fraction decomposition of the rational expression # x / (x² - x - 2)#?
• How do you write the partial fraction decomposition of the rational expression #x^2 / (x² + x + 2)#?
• How do you write the partial fraction decomposition of the rational expression # (x+4)/((x+1)(x-2)^2 )#?
• How do you write the partial fraction decomposition of the rational expression # 1/(x^2+x+1) #?
• How do you write the partial fraction decomposition of the rational expression #(x^3 + x) /(x^2 + x + 1)^2#?
• How do you write the partial fraction decomposition of the rational expression #[((3x^2)+3x+12) / ((x-5)(x^2+9))]#?
• How do you write the partial fraction decomposition of the rational expression # 10/[(x-1)(x^2+9)] #?
• How do you write the partial fraction decomposition of the rational expression # (x^3 - 6x^2 + 11x - 6) / (4x^3 - 28x^2 + 56x - 32) #?
• How do you write the partial fraction decomposition of the rational expression # (4x+4)/(x^2(x+2))#?
• How do you write the partial fraction decomposition of the rational expression #( 3x) /( x^3 − 2x^2 − x + 2)#?
• How do you write the partial fraction decomposition of the rational expression #(x^2 + 2) /( x^3 + 3x^2 + 3x + 1)#?
• How do you write the partial fraction decomposition of the rational expression #(x^2 − x + 1 )/( x^3 − x^2 + x − 1)#?
• How do you write the partial fraction decomposition of the rational expression #(-13x+11) / (2x^3 - 2x^2 + x - 1)#?
• How do you write the partial fraction decomposition of the rational expression #8 / [ ( x + 2 ) ( x^2 + 4 ) ]#?
• How do you write the partial fraction decomposition of the rational expression #(x+6)/(x^3-3x^2-4x+12)#?
• How do you write the partial fraction decomposition of the rational expression #(4x^2+ 21x-22)/((2x-1)(x^2 +x-42))#?
• How do you write the partial fraction decomposition of the rational expression #(s^3+s-4)/( (s^2+1)(s^2+4))#?
• How do you write the partial fraction decomposition of the rational expression #(3x^2+2x)/(x^2-4)#?
• How do you write the partial fraction decomposition of the rational expression #(x - 16) / (x^2 + x - 2)#?
• How do you write the partial fraction decomposition of the rational expression # 3/(x ^(2) + 16x +5)#?
• How do you write the partial fraction decomposition of the rational expression # (2x^3-x^2+x+5)/(x^2+3x+2)#?
• How do you write the partial fraction decomposition of the rational expression # (4x+23)/(x^2-x-6)#?
• How do you write the partial fraction decomposition of the rational expression # (x+4)/[(x+1)^2 + 4]#?
• How do you write the partial fraction decomposition of the rational expression # (x^3 - 2) / (x^4 - 1)#?
• How do you write the partial fraction decomposition of the rational expression # (x^2 - 3x) / ((x-1)(x+2))#?
• How do you write the partial fraction decomposition of the rational expression # (x^3+2)/(x^2-x)#?
• How do you write the partial fraction decomposition of the rational expression # (x+1)/(x^2(x-2))#?
• How do you write the partial fraction decomposition of the rational expression # 1/(x^3-6x^2+9x) #?
• How do you write the partial fraction decomposition of the rational expression # (x+10)/(x^2+2x-8)#?
• How do you write the partial fraction decomposition of the rational expression # (5x+7)/(x^2+4x-5)#?
• How do you write the partial fraction decomposition of the rational expression # 1/((x^4)-6(x^3))#?
• How do you write the partial fraction decomposition of the rational expression # (8x-1)/(x^3 -1)#?
• How do you write the partial fraction decomposition of the rational expression # x/ (x^3-2x+x)#?
• How do you write the partial fraction decomposition of the rational expression #(2x - 3) / (x - 1)^2 #?
• How do you write the partial fraction decomposition of the rational expression #3 / (x^2 - 3x)#?
• How do you write the partial fraction decomposition of the rational expression #5 / (x^2 + x - 6)#?
• How do you write the partial fraction decomposition of the rational expression #(x + 2) /( x(x - 4))#?
• How do you write the partial fraction decomposition of the rational expression #1/ [(x-1) ( x+ 1) ^2]#?
• How do you write the partial fraction decomposition of the rational expression #(x^3-x^2+1) / (x^4-x^3)#?
• How do you write the partial fraction decomposition of the rational expression #(9x^2+9x+40)/(x(x^2+5))#?
• How do you write the partial fraction decomposition of the rational expression #(7 x^2 - 7 x+12)/(x^4+x^2-2)#?
• How do you write the partial fraction decomposition of the rational expression #(x^2 + 5x - 7 )/( x^2 (x+ 1)^2)#?
• How do you write the partial fraction decomposition of the rational expression #x/((x-1)(x^2+4)#?
• How do you write the partial fraction decomposition of the rational expression # [(3x)/(x^2-6x+9)]#?
• How do you write the partial fraction decomposition of the rational expression # (4x-1 )/( x^2+3x-4)#?
• How do you write the partial fraction decomposition of the rational expression # x^2 /(x^2 +x+2)#?
• How do you write the partial fraction decomposition of the rational expression # (2x+1)/(4x^2+12x-7)#?
• How do you write the partial fraction decomposition of the rational expression # 2 / (x^3 + 1)#?
• How do you write the partial fraction decomposition of the rational expression #(5x - 1) / ((x - 2)(x + 1))#?
• How do you write the partial fraction decomposition of the rational expression #(x^2)/(x+1)^3#?
• How do you write the partial fraction decomposition of the rational expression #(3x^2 + 10x -5)/ ( (x+1)^2(x-2) )#?
• How do you write the partial fraction decomposition of the rational expression #(x-2) /( x^2+4x+3)#?
• How do you write the partial fraction decomposition of the rational expression #1/((x+7)(x^2+9))#?
• How do you write the partial fraction decomposition of the rational expression #(5x^3 -9x+6)/(x^3-x^2)#?
• How do you write the partial fraction decomposition of the rational expression #(10x + 2)/ (x^3 - 5x^2 + x - 5)#?
• How do you write the partial fraction decomposition of the rational expression #(3x^2 -7x+1) / (x-1)^3#?
• How do you write the partial fraction decomposition of the rational expression #x/ (8x^2−6x+1)#?
• How do you write the partial fraction decomposition of the rational expression #x^2/((x-1)(x+2))#?
• How do you write the partial fraction decomposition of the rational expression #(3x^2 + 4x) / (x^2 +1)^2#?
• How do you write the partial fraction decomposition of the rational expression #(-3x^2-5x+18)/((x+1)(x^2+9))#?
• How do you write the partial fraction decomposition of the rational expression #7/(x^2-14x)#?
• How do you write the partial fraction decomposition of the rational expression #(4x^2+3)/((x-5)^3)#?
• How do you write the partial fraction decomposition of the rational expression #(x+1)/( (x^2 )*(x-1) )#?
• How do you write the partial fraction decomposition of the rational expression # x/(x^3-x^2-6x)#?
• How do you write the partial fraction decomposition of the rational expression # (x^2+8)/(x^2-5x+6)#?
• How do you write the partial fraction decomposition of the rational expression # (x+13)/(x^3+2x^2-5x-6)#?
• How do you write the partial fraction decomposition of the rational expression # (-4x-2)/((x-4)(x-7))#?
• How do you write the partial fraction decomposition of the rational expression # (7x^2 - 12x + 11) / (2x^3 - 5x^2 + x +2)#?
• How do you write the partial fraction decomposition of the rational expression # (9x) / (x^2 + 2x - 8)#?
• How do you write the partial fraction decomposition of the rational expression # (x^2 + 4)/ ((x^2 - 4)(x^2 +2))#?
• How do you write the partial fraction decomposition of the rational expression # (x^2+x)/((x+2)(x-1)^2)#?
• How do you write the partial fraction decomposition of the rational expression # (8x^2 - 4x - 8)/(x^4 + 2x^3)#?
• How do you write the partial fraction decomposition of the rational expression # (x^2)/(x+1)^3#?
• How do you write the partial fraction decomposition of the rational expression #(2x-6)/((x-1)(x-2)^2)#?
• How do you write the partial fraction decomposition of the rational expression #x^2 / ((x-1)^2 (x+1))#?
• How do you express # f(x) = (3x + 2) / [(x - 1)(x + 4)]# in partial fractions?
• How do you express #(1) / (x * ( x^2 - 1 )^2) # in partial fractions?
• How do you express #(3x)/((x + 2)(x - 1))# in partial fractions?
• How do you express #(x^5 + 1)/(x^6 - x^4)# in partial fractions?
• How do you express #1 / ((x+5)^2 (x-1)) # in partial fractions?
• How do you express #x^4/(x-1)^3# in partial fractions?
• How do you express #(5x-1)/(x^2-x-2)# in partial fractions?
• How do you express # (3x+18)/(x^2+5x+4)# in partial fractions?
• How do you express #(x^2-1)/((x)*(x^2+1) )# in partial fractions?
• How do you express #x^3/(x^2 + 4x + 3 )# in partial fractions?
• How do you express #1/ (x^4 +1)# in partial fractions?
• How do you express #3/ (x^2-6x+8)# in partial fractions?
• How do you express #2/(x^3-x^2)# in partial fractions?
• How do you express #x^3/[x(x^2+2x+1)]# in partial fractions?
• How do you express #(x^3+x^2+x+2)/(x^4+x^2)# in partial fractions?
• How do you express #1/((x+7)(x^2+9))# in partial fractions?
• How do you express #(x+1)/(x^2 + 6x)# in partial fractions?
• How do you express #(2x^3 -x^2)/((x^2 +1)^2)# in partial fractions?
• How do you express #(3x )/ (x^2 * (x^2+1) )# in partial fractions?
• How do you express # 1/(1+e^x) # in partial fractions?
• How do you express #x/((x-1)(x^2+4)# in partial fractions?
• How do you express #(x^2-2x+1)/(x-2)^3# in partial fractions?
• How do you express #(2x - 1) / [(x - 1)^3 (x - 2)]# in partial fractions?
• How do you express #(4x^3) / (x^3 + 2x^2 - x - 2)# in partial fractions?
• How do you express #(x^2 - 3x) / ((x-1)(x+2))# in partial fractions?
• How do you express #(2x+ 3)/(x^4-9x^2)# in partial fractions?
• How do you express #(x^3)/(x^3+1)# in partial fractions?
• How do you express #(2x^2+5)/(x^2+1)^2# in partial fractions?
• How do you express #(x-1)/(x^3 +x)# in partial fractions?
• How do you express #x/(16x^4-1)# in partial fractions?
• How do you express # (5x^2+3x-2)/(x^3+2x^2) # in partial fractions?
• How do you express # (4x-1)/( x^2(x-4))# in partial fractions?
• How do you express #(x-1)/(1+x^2)# in partial fractions?
• How do you express #(x^2+x)/((x+2)(x-1)^2)# in partial fractions?
• How do you express #(6x^2+1)/(x^2(x-1)^2)# in partial fractions?
• How do you express #1/(x^3 +4x)# in partial fractions?
• How do you express # [(3x)/(x^2-6x+9)]# in partial fractions?
• How do you express #(4x-2) /( 3(x-1)^2)# in partial fractions?
• How do you express #1/(x^3-1)# in partial fractions?
• How do you express #(6x^2+8x+30)/(x^3-27)# in partial fractions?
• How do you express #(x-1)/(x^3 +x^2)# in partial fractions?
• How do you express #(x^3-x^2+1) / (x^4-x^3)# in partial fractions?
• How do you express #(2(1-x-x^2))/(1-x^2)# in partial fractions?
• How do you express #(x^2 + 33)/(x^3 + x^2)# in partial fractions?
• How do you express #(-2x-3)/(x^2-x) # in partial fractions?
• How do you express #(x^3+1) / (x^2+4)# in partial fractions?
• How do you express #1/(4x^2 - 9)# in partial fractions?
• How do you express #(x^2) / ( x^2 + 3x +2) # in partial fractions?
• How do you express #(3x-1)/(x^2-x)# in partial fractions?
• How do you express #(x+13)/(x^3+2x^2-5x-6)# in partial fractions?
• How do you express #1/(x^2+x+1) # in partial fractions?
• How do you express # (2x - 1) / [(x - 1)^3 (x - 2)]# in partial fractions?
• How do you express # 2 / (x^3 + 1)# in partial fractions?
• How do you express #1/[(x^3)-1]# in partial fractions?
• How do you express #(x^2)/(x+1)^3# in partial fractions?
• How do you express #(2x) / (4x^2 + 12x + 9)# in partial fractions?
• How do you express #(4x^2+6x-2)/((x-1)(x+1)^2)# in partial fractions?
• How do you express #x^2/(x^2 + x +2)# in partial fractions?
• How do you express #(8x-1)/(x^3 -1)# in partial fractions?
• How do you express # x/ (x^3-2x^2+x)# in partial fractions?
• How do you express #(x^3 - 5x + 2) / (x^2 - 8x + 15)# in partial fractions?
• How do you express #1/(x^4 - 16)# in partial fractions?
• How do you express #1/((x+6)(x^2+3))# in partial fractions?
• How do you express #(x^2-2x-1) / ((x-1)^2 (x^2+1))# in partial fractions?
• How do you express #(3x) / (x-3)^2# in partial fractions?
• How do you express # (x+2) / (x(x-4))# in partial fractions?
• How do you express #(x^(2) - 1) / (x(x^(2)+1))# in partial fractions?
• How do you express # (x) / (x^(3)-x^(2)-2x +2)# in partial fractions?
• How do you express #(x+4)/(x^2 + 2x + 5)# in partial fractions?
• How do you express #(9x)/(9x^2+3x-2)# in partial fractions?
• How do you express #1/(e^x(e^x+1))# in partial fractions?
• How do you express #1/[(1+x)(1-2x)]# in partial fractions?
• How do you express #(x+1 )/[ x^2(x-2)]# in partial fractions?
• How do you express #(-7x^2-15x-8)/((x+3)(x^2+4))# in partial fractions?
• How do you express #(x^3-x^2-5x) /( x^2-3x+2)# in partial fractions?
• How do you express #(x^2)/((x^4) - (2x^2) - 8)# in partial fractions?
• How do you express #(17x-50)/(x^(2)-6x+8)# in partial fractions?
• How do you express #1/(x^3-6x^2+9x)# in partial fractions?
• How do you express #(3x+2) / (x^(2)+3x-4)# in partial fractions?
• How do you express #(x^4+1)/(x^5+6 x^3)# in partial fractions?
• How do you express #6/(x^2-25)^2# in partial fractions?
• How do you express # (x^3 + 2) / (x^4 -16)# in partial fractions?
• How do you express # (6x^2+7x-6)/((x^2-4)(x+2))# in partial fractions?
• How do you express # (5x^2+7x-4)/(x^3+4x^2)# in partial fractions?
• How do you express # (3x^2 - 4x - 2) / [(x-1)(x-2)]# in partial fractions?
• How do you express # (11x-2) /( x^2 + x-6)# in partial fractions?
• How do you express #(3x)/(x^2+x-2)# in partial fractions?
• How do you express #( x-2 ) / (x^2 + 4x + 3)# in partial fractions?
• How do you express #(6x+5) / (x+2) ^4# in partial fractions?
• How do you express #(x+4)/((x+1)(x-2)^2)# in partial fractions?
• How do you express # (x^2-16x+9)/(x^4+10x^2+9)# in partial fractions?
• How do you express #(x^3 +1)/ (x^2 +3) # in partial fractions?
• How do you express #1/ (x^2 + 3x -4)# in partial fractions?
• How do you express #(5x - 4 ) / (x^2 -4x) # in partial fractions?
• How do you express #1/ [ (x-1)(x+2)(x-3)] # in partial fractions?
• How do you express #(x^2 - 4) / (x -1)# in partial fractions?
• How do you express #(2x^5 -x^3 -1) / (x^3 -4x) # in partial fractions?
• How do you express #(x^3+4)/[x^2+4] # in partial fractions?
• How do you express #10 / [(x-1)(x^2 + 9)]# in partial fractions?
• How do you express #(4x^5 + 2x^4 + 3x^3 - x^2 - x + 1) /( x (x^2 + 1))# in partial fractions?
• How do you express #x^2 / (x-1)^3# in partial fractions?
• How do you express #2 / (x(4x-1))# in partial fractions?
• How do you express # (5x^2 - 25x + 28) / (x^2(x-7))# in partial fractions?
• How do you express #(y^2 + 1) / (y^3 - 1)# in partial fractions?
• How do you express #(2x^3-x^2+x+5)/(x^2+3x+2) # in partial fractions?
• How do you express #1/((x²)(x² + 3x + 2)) # in partial fractions?
• How do you express #(x+1)/( (x^2 )*(x-1) )# in partial fractions?
• How do you express # x/(x^3-x^2-6x)# in partial fractions?
• How do you express #(x^2+8)/(x^2-5x+6)# in partial fractions?
• How do you express #(x^2) / (x^2+x+2)# in partial fractions?
• How do you express #(2x-2)/((x-5)(x-3))# in partial fractions?
• How do you express #(x^4)/((x²+1)(x²-1))# in partial fractions?
• How do you express #(2x^4 + 9x^2 + x - 4)/(x^3 + 4x)# in partial fractions?
• How do you express #(x³ - 7x - 3)/(x² - x -2) # in partial fractions?
• How do you express #(x²+2) / (x+3) # in partial fractions?
• How do you express # [((3x^2)+3x+12) / ((x-5)(x^2+9))]# in partial fractions?
• How do you express #(x^2 - 8x + 44) / ((x + 2) (x - 2)^2)# in partial fractions?
• How do you express #(4x^2 - 7x - 12) / ((x) (x+2) (x-3))# in partial fractions?
• How do you express #(-2x-3)/(x^2-x) # in partial fractions?
• How do you express #(x^2 - 3x + 2) / (4x^3 + 11x^2)# in partial fractions?
• How do you express #(x² + 2x-7 )/( (x+3)(x-1)²)# in partial fractions?
• How do you express #3/((x-2)(x+1))# in partial fractions?
• How do you express # ( x^2 + 2 ) / (x+2) # in partial fractions?
• How do you express #x/((x-1)(x+1)) # in partial fractions?
• How do you express #(13x + 2)/( x^3 -1) # in partial fractions?
• How do you express #x+22 div x^2+2x-8# in partial fractions?
• How do you express #3/((1 + x)(1 - 2x)) # in partial fractions?
• How do you express #((x^3+1)/(x^2+3))# in partial fractions?
• How do you express # (x^3 +x^2+2x+1) / [(x^2+1) (x^2+2)]# in partial fractions?
• How do you express # (3x+5)/((3x+2)(2x+1) )# in partial fractions?
• How do you express #(x^4+6)/(x^5+7x^3)# in partial fractions?
• How do you express #(2x^2+4x+12)/(x^2+7x+10)# in partial fractions?
• How do you express #(2x^2-18x-12)/(x^3-4x)# in partial fractions?
• How do you express # 1 / (x^6 - x^3)# in partial fractions?
• How do you express #(x+4)/[(x+1)^2 + 4]# in partial fractions?
• How do you express #1/(x^3-4x)# in partial fractions?
• How do you express # (x^3)/((x^2)-1)# in partial fractions?
• How do you express #(4x^3-22x^2+33x-6)/((x-3)^3(x+2))# in partial fractions?
• How do you express #x/((x^2-1)(x-1))# in partial fractions?
• How do you express #(x+1)/[(x^2+1)^2(x^2)]# in partial fractions?
• How do you express # (x^2 + 2x) / (x^3 - x^2 + x - 1) # in partial fractions?
• How do you express #(x^3+x^2+2x+1)/((x^2+1)(x^2+2))# in partial fractions?
• How do you express #( 1+2x )/( (6x^2+1)(1-3x))# in partial fractions?
• How do you express # (x + 2)/((2x+7)(x+1))# in partial fractions?
• How do you express #(x-9)/[(x+5)(x-2)] # in partial fractions?
• How do you express #(-5s-36) / [ (s+2) (s^2+9) ]# in partial fractions?
• How do you express # x^2/(x^2+9)^2# in partial fractions?
• How do you express # (7x-2)/((x-3)^2(x+1))# in partial fractions?
• How do you write the fractional decomposition of #(5x^2 + 7x + 3)/(x^3 + x)#?
• How do you decompose #(3p-1)/(p^2-1)# into partial fractions?
• How do you decompose #(x-6)/(x^2-2x)# into partial fractions?
• How do you decompose #(5m-4)/(m^2-4)# into partial fractions?
• How do you decompose #(-4y)/(3y^2-4y+1)# into partial fractions?
• How do you solve #2/(x^2-16x+64)-8/(x-7)=(Ax+B)/(x^2-16x+63)#?
• How do you write the partial fraction decomposition of #(2x^3-x^2+x+5)/(x(x+1)^2)#?
• Question #31f48
• Find the partial fraction decomposition of #(x^3+x^2+x+2)/(x^4+x^2)#?
• Question #7fec7
• How to solve #sum_(n=1)^oo 1/((3n-2)(3n+1))# using partial fractions?
• Can someone explain me this please?
• How do you evaluate #\frac { ( x + 1) ^ { 2} } { ( x - 2) ( x - 1) ^ { 2} } = \frac { A } { x - 2} + \frac {B}{x-1}+\frac { c } { ( x - 1) ^ { 2} }#?
• How do I split this into partial fractions?