Answer
$\displaystyle \frac{5x+1}{(x-1)^{2}(x+1)^{2}}$
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 = $(x-1)^{2}(x+1)^{2}$
Step 3:
Write each rational expression using the LCM as the denominator. Simplify.
$\displaystyle \frac{3}{(x-1)^{2}(x+1)}\cdot\frac{(x+1)}{(x+1)}+\frac{2}{(x-1)(x+1)^{2}}\cdot\frac{(x-1)}{(x-1)}$
$=\displaystyle \frac{3x+3+2x-2}{(x-1)^{2}(x+1)^{2}}$
$=\displaystyle \frac{5x+1}{(x-1)^{2}(x+1)^{2}}$
