How can I solve this partial fraction 7x104x212x+9?

1 Answer
Aug 1, 2018

7x104x212x+9=72(2x3)+12(2x3)2

Explanation:

Given:

7x104x212x+9

First note that:

4x212x+9=(2x3)2

is a perfect square trinomial.

So we are looking for a partial fraction expansion of the form:

7x104x212x+9=A2x3+B(2x3)2

Mutiplying both sides by (2x3)2, this becomes:

7x10=A(2x3)+B

Looking at the coefficient of x, we can deduce that:

A=72

Putting x=32, we find:

B=7(32)10=12

So:

7x104x212x+9=72(2x3)+12(2x3)2