Answer
$-\dfrac{1}{2(x+1)}+\dfrac{3}{2(x-1)} $
Work Step by Step
We will write the partial decomposition as:
$\dfrac{x+2}{(x+1)(x-1)}=\dfrac{A}{x+1}+\dfrac{B}{x-1} ~~~~(a)$
This implies that $x+2=A(x-1)+B (x+1)$
Plug $x=-1$ to obtain: $A=-\dfrac{1}{2}$
Now, plug $x=1$ to obtain: $B=\dfrac{3}{2}$
So, the equation (a) becomes:
$\dfrac{x+2}{(x+1)(x-1)}=-\dfrac{1}{2(x+1)}+\dfrac{3}{2(x-1)} $
