Question

How do you write the partial fraction decomposition of the rational expression `( x-5)/(x-2)^2`?

Answer 1

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

Explanation:

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