How do you express $\frac{1}{x^{3} + 4 x}$ $1/(x^3 +4x)$ in partial fractions?

Question

How do you express $\frac{1}{x^{3} + 4 x}$ $1/(x^3 +4x)$ in partial fractions?

1 Answer

Related questions

What does partial-fraction decomposition mean?
What is the partial-fraction decomposition of $\frac{5 x + 7}{x^{2} + 4 x - 5}$ $(5x+7)/(x^2+4x-5)$ ?
What is the partial-fraction decomposition of $\frac{x + 11}{(x + 3) (x - 5)}$ $(x+11)/((x+3)(x-5))$ ?
What is the partial-fraction decomposition of $\frac{x^{2} + 2 x + 7}{x {(x - 1)}^{2}}$ $(x^2+2x+7)/(x(x-1)^2)$ ?
How do you write $\frac{2}{x^{3} - x^{2}}$ $2/(x^3-x^2)$ as a partial fraction decomposition?
How do you write $\frac{x^{4}}{{(x - 1)}^{3}}$ $x^4/(x-1)^3$ as a partial fraction decomposition?
How do you write $\frac{3 x}{(x + 2) (x - 1)}$ $(3x)/((x + 2)(x - 1))$ as a partial fraction decomposition?
How do you write the partial fraction decomposition of the rational expression $\frac{x^{2}}{x^{2} + x + 4}$ $x^2/ (x^2+x+4)$ ?
How do you write the partial fraction decomposition of the rational expression # (3x^2 + 12x -...
How do you write the partial fraction decomposition of the rational expression $\frac{1}{(x + 6) (x^{2} + 3)}$ $1/((x+6)(x^2+3))$ ?

Impact of this question

2902 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-05T01:33:09

let
$\frac{1}{x^{3} + 4 x} = \frac{1}{x (x^{2} + 4)} = \frac{a}{x} + \frac{b x}{x^{2} + 4} = \frac{a (x^{2} + 4) + b x^{2}}{x (x^{2} + 4)}$ $1/(x^3+4x)=1/(x(x^2+4))=a/x+(bx)/(x^2+4)=(a(x^2+4)+bx^2)/(x(x^2+4))$
Now
$1 = (a (x^{2} + 4) + b x^{2})$ $1=(a(x^2+4)+bx^2)$
putting x=0 in the above identity we have $4 a = 1 \Rightarrow a = \frac{1}{4}$ $4a=1 =>a=1/4$
Again putting x=1, we have $5 a + b = 1$ $5a+b=1$
putting $a = \frac{1}{4}$ $a=1/4$ in the 2nd equation $5 a + b = 1$ $5a+b=1$
we get $\frac{5}{4} + b = 1 \Rightarrow b = - \frac{1}{4}$ $5/4+b=1=>b=-1/4$

Hence we can write
$\frac{1}{x^{3} + 4 x} = \frac{1}{4} (\frac{1}{x} - \frac{x}{x^{2} + 4})$ $1/(x^3+4x)=1/4(1/x-x/(x^2+4))$

Science

Math

Humanities

... and beyond

How do you express $\frac{1}{x^{3} + 4 x}$ $1/(x^3 +4x)$ in partial fractions?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you express 1x3+4x1/(x^3 +4x) in partial fractions?

1 Answer

Related questions

Impact of this question

How do you express $\frac{1}{x^{3} + 4 x}$ $1/(x^3 +4x)$ in partial fractions?