`(x+5)/((x+3)^2)` `=A/(x+3)+B/((x+3)^2)`

Multiply both sides by `(x + 3)^2`:

`x + 5 = A(x + 3) + B`

Equating `x` parts and constant parts:

`1 = A`

`5 = 3A + B`

So `B = 2`.

So

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

Don't believe it is true! Add the right hand side and convince yourself about the accuracy of this process. You actually learn a lot about how it works by doing this. And it's always good to check your work!