I have the problem.
Let $f(t) = \frac{t - x}{t + y}.$
Show that $f(x + y) + f(x - y) = \frac{-2y^2}{x^2 + 2xy}.$
I know that this is just some substitution followed by simplification, but am missing the point of the let $f(t) = (t - x)/(t + y)$. It doesn't seem to fit into the "show that" portion of the question. Can someone steer me in the right direction?