Answer
$\dfrac{A}{x-1}+\dfrac{B}{x+2}$
Work Step by Step
Simplify $\dfrac{1}{(x-1)(x+2)}$ into partial fraction decomposition.
This shows a single linear functions.
Applying the partial fraction decomposition rule.
$\dfrac{1}{(x-1)(x-2)}=\dfrac{A}{x-1}+\dfrac{B}{x+2}$