Answer
$\displaystyle \frac{-2(2x+7)}{(x-1)^{2}(x+2)^{2}}$
Work Step by Step
Step 1:
Factor each denominator
... both are given in factored form
Step 2: The LCM is the product of each of these factors raised to a power equal to the greatest number of times that the factor occurs in the polynomials.
LCM = $(x-1)^{2}(x+2)^{2}$
Step 3:
Write each rational expression using the LCM as the denominator. Simplify.
$\displaystyle \frac{2}{(x+2)^{2}(x-1)}\cdot\frac{(x-1)}{(x-1)}-\frac{6}{(x+2)(x-1)^{2}}\cdot\frac{(x+2)}{(x+2)}$
$=\displaystyle \frac{2x-2-6x-12}{(x-1)^{2}(x+2)^{2}}$
$=\displaystyle \frac{-4x-14}{(x-1)^{2}(x+2)^{2}}$
$=\displaystyle \frac{-2(2x+7)}{(x-1)^{2}(x+2)^{2}}$
