Simplify:
$\displaystyle
\frac{1}{x - y} + \frac{2 x - y}{x^2 - y^2} $
$\displaystyle
\frac{1}{x - y} + \frac{2 x - y}{x^2 - y^2}
$
= $\displaystyle
\frac{1}{x - y} + \frac{2 x - y}{(x + y)(x - y)}
$
= $\displaystyle
\frac{x^2 - y^2}{x - y} + \frac{(2 x - y)(x - y)}{(x + y)(x - y)}
$
= $\displaystyle
\frac{x^2 - y^2 + 2 x^2 - 2 x y - x y - y^2}{(x - y)(x + y)(x - y)}
$
= $\displaystyle
\frac{x^2 - y^2 + 2 x^2 - 3 x y - y^2}{(x - y)(x + y)(x - y)}
$
= $\displaystyle
\frac{3 x^2 - 2 y^2 - 3 x y}{(x - y)(x + y)(x - y)}
$
I'm not sure what you're asking.
You get each fraction over a common denominator. The common denominator is (x + y)(x - y). Only one fraction needs to be re-written so that it is has the common denominator. I did that. The other fraction already has the common denominator - so nothing gets done to it.