Answer
$\dfrac{5x+1}{(x-1)^2(x+1)^2}$
Work Step by Step
The LCD is $(x-1)^2(x+1)^2$.
Make the expressions similiar by multiplying $x+1$ to both the numerator and denominator fo the first expression and $x-1$ to the second expresions to obtain:
$=\dfrac{3(x+1)}{(x-1)^2(x+1)^2}+\dfrac{2(x-1)}{(x-1)^2(x+1)^2}$
Add numerators and retain the denominator:
$=\dfrac{3(x+1)+2(x-1)}{(x-1)^2(x+1)^2}$
Use distributive property.
$=\dfrac{3x+3+2x-2}{(x-1)^2(x+1)^2}$
$=\dfrac{5x+1}{(x-1)^2(x+1)^2}$
Hence, the lowest term is:
$\dfrac{5x+1}{(x-1)^2(x+1)^2}$
