Question

How do you write the partial fraction decomposition of the rational expression `(2x-3) / (x-1)^2`?

Answer 1

`(2x-3)/(x-1)^2=2/(x-1)-1/(x-1)^2`

Explanation:

`(2x-3)/(x-1)^2=A/(x-1)+B/(x-1)^2`
`2x-3=A(x-1)+B`
`x=1->-1=B`
Comparing coefficients of the `x` term on both sides, we see that `A=2`
Therefore, `(2x-3)/(x-1)^2=2/(x-1)-1/(x-1)^2`