Answer
$-\dfrac{2(2x+7)}{(x+2)^2(x-1)^2}$
Work Step by Step
The LCD is $(x+2)^2(x-1)^2$.
Make the expressions similar by multiplying $x-1$ to both the numerator and denominator of the first expression and $x+2$ to the second expression to obtain:
$=\dfrac{2(x-1)}{(x+2)^2(x-1)^2}-\dfrac{6(x+2)}{(x+2)^2(x-1)^2}$
Subtract the numerators and retain the denominator:
$=\dfrac{2(x-1)-6(x+2)}{(x+2)^2(x-1)^2}$
Use distributive property.
$=\dfrac{2x-2-6x-12}{(x+2)^2(x-1)^2}$
$=\dfrac{-4x-14}{(x+2)^2(x-1)^2}$
Factor the numerator.
$=-\dfrac{2(2x+7)}{(x+2)^2(x-1)^2}$
Hence, the lowest term is:
$-\dfrac{2(2x+7)}{(x+2)^2(x-1)^2}$
