If x + y = 2a, then the value of ax - a + ay - a\, is = ?

Answer: Option B

$$\begin{array}{rl}& \text{Given, }\\ & x+y=2a\\ & \therefore \frac{a}{x-a}+\frac{a}{y-a}\\ & =\frac{a\left(y-a\right)+a\left(x-a\right)}{\left(x-a\right)\left(y-a\right)}\\ & =\frac{ay-a^2+ax-a^2}{\left(x-a\right)\left(y-a\right)}\\ & =\frac{a\left(x+y\right)-2a^2}{\left(x-a\right)\left(y-a\right)}\\ & =\frac{a.2a-2a^2}{\left(x-a\right)\left(y-a\right)}\\ & =\frac{2a^2-2a^2}{\left(x-a\right)\left(y-a\right)}\\ & =0\end{array}$$