Answer
$\frac{-6x+21}{(x-2)(x+1)}$
Work Step by Step
By inspection, we see that the LCM of the denominators is $(x-2)(x+1)$. Therefore, we create a common denominator using this LCM and obtain:
$\frac{3}{x-2}-\frac{9}{x+1}$
=$\frac{3(x+1)-9(x-2)}{(x-2)(x+1)}$
=$\frac{3x+3-9x+18}{(x-2)(x+1)}$
=$\frac{-6x+21}{(x-2)(x+1)}$
