If $x + y = 2a$, then the value of $\frac{a}{x-a} + \frac{a}{y-a}$ is -

Explanation

$$ \begin{aligned} \frac{a}{x-a} + \frac{a}{y-a} &= \frac{ay - a^2 + ax - a^2}{(x-a)(y-a)} \\ &= \frac{a(x+y) - 2a^2}{(x-a)(y-a)} \\ &= \frac{a(2a) - 2a^2}{(x-a)(y-a)} \quad [\because x+y=2a] \\ &= \frac{2a^2 - 2a^2}{(x-a)(y-a)} \\ &= \frac{0}{(x-a)(y-a)} \\ &= 0 \end{aligned} $$