\[\frac{2^{\backslash x + y}}{x - y} + \frac{4^{\backslash x - y}}{x + y} = \frac{2x + 2y + 4x - 4y}{(x - y)(x + y)} =\]
\[= \frac{6x - 2y}{x^{2} - y^{2}}\]