Answer
$\dfrac{1}{6(x-1)}+\dfrac{5}{6(x+5)} $
Work Step by Step
We will write the partial decomposition as:
$\dfrac{x}{(x-1)(x+5)}=\dfrac{A}{x-1}+\dfrac{B}{x+5} ~~~~(a)$
This implies that $x=A(x+5)+B (x-1)$
Plug $x=1$ to obtain: $A=\dfrac{1}{6}$
Now, plug $x=-5$ to obtain: $B=\dfrac{5}{6}$
So, the equation (a) becomes:
$\dfrac{x}{(x-1)(x+5)}=\dfrac{1}{6(x-1)}+\dfrac{5}{6(x+5)} $
