Question

Question #31f48

Answer 1

The answer is `=3/(x-1)^2+5/(x-1)`

Explanation:

Let's do the partial fraction decomposition

`(5x-2)/(x-1)^2=A/(x-1)^2+B/(x-1)`

`=(A+B(x-1))/(x-1)^2`

The denomintors are the same, so we equalise the nunerators

`5x-2=A+B(x-1)`

Coefficients of x, `5=B`

Let `x=1`, `=>`, `3=A`

Therefore,

`(5x-2)/(x-1)^2=3/(x-1)^2+5/(x-1)`