How do you express x^2/(x^2+9)^2x2(x2+9)2 in partial fractions?

1 Answer
Shwetank Mauria
Apr 13, 2016

x^2/(x^2+9)^2hArr1/(x^2+9)-9/(x^2+9)^2x2(x2+9)2⇔1x2+9−9(x2+9)2

Explanation:

Partial fractions of x^2/(x^2+9)^2x2(x2+9)2 will be of type

x^2/(x^2+9)^2hArr(Ax+B)/(x^2+9)+(Cx+D)/(x^2+9)^2x2(x2+9)2⇔Ax+Bx2+9+Cx+D(x2+9)2

Simplifying RHS

x^2/(x^2+9)^2hArr((Ax+B)(x^2+9)+Cx+D)/(x^2+9)^2x2(x2+9)2⇔(Ax+B)(x2+9)+Cx+D(x2+9)2 or

x^2/(x^2+9)^2hArr(Ax^3+Bx^2+9Ax+9B+Cx+D)/(x^2+9)^2x2(x2+9)2⇔Ax3+Bx2+9Ax+9B+Cx+D(x2+9)2

Now comparing like terms on each side

A=0A=0, B=1B=1, 9A+C=09A+C=0 and 9B+D=09B+D=0

As A=0A=0 and B=1B=1, putting these values we get C=0C=0 and D=-9D=−9.

Hence x^2/(x^2+9)^2hArr1/(x^2+9)-9/(x^2+9)^2x2(x2+9)2⇔1x2+9−9(x2+9)2

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