Answer
$3(x+y)$.
Work Step by Step
The given expression is
$=\frac{3x^2}{x-y}+\frac{3y^2}{y-x}$.
Rewrite as shown below.
$=\frac{3x^2}{x-y}+\frac{3y^2}{-(x-y)}$
$=\frac{3x^2}{x-y}-\frac{3y^2}{x-y}$
Add numerators because both denominators are equal.
$=\frac{3x^2-3y^2}{x-y}$
Factor $3x^2-3y^2$.
$=3(x^2-y^2)$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$.
$=3(x+y)(x-y)$
Substitute the factor into the fraction.
$=\frac{3(x+y)(x-y)}{x-y}$
Cancel common terms.
$=3(x+y)$.
