How do you express (2x^3 -x^2)/((x^2 +1)^2) in partial fractions?

1 Answer
Feb 14, 2016

Partial fractions are (2x+1)/(x^2+1)-(2x+1)/(x^2+1)^2

Explanation:

Let the function (2x^3-x^2)/(x^2+1)^2 be written in partial fractions as

(Ax+B)/(x^2+1)+(Cx+D)/(x^2+1)^2

Solving this becomes ((Ax+B)(x^2+1)+Cx+D)/(x^2+1)^2

As denominator in given function is same

it follows that

(Ax+B)(x^2+1)+Cx+DhArr(2x^3-x^2) or

Ax^3+Bx^2+(A+C)x+(B+D)hArr(2x^3-x^2)

Comparing like terms

A=2, B=-1, A+C=0 and B+D=0 i.e.

A=2, B=-1, C=-2 and D=-1

Hence partial fractions are (2x+1)/(x^2+1)-(2x+1)/(x^2+1)^2