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

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given, }}x + y = 2a \cr & {\text{Find, }}\frac{a}{{x - a}} + \frac{a}{{y - a}}{\text{ = ?}} \cr & \mathop {\mathop x\limits_ \downarrow \,}\limits_3 + \mathop {\mathop y\limits_ \downarrow }\limits_1 = \mathop {\mathop {2a}\limits_ \downarrow }\limits_2 \cr & {\text{Let }}x = 3,{\text{ }}y = 1,{\text{ }}a = 2 \cr & \therefore \frac{a}{{x - a}} + \frac{a}{{y - a}} \cr & = \frac{2}{{\left( {3 - 2} \right)}} + \frac{2}{{\left( {1 - 2} \right)}} \cr & = \frac{2}{1} + \frac{2}{{ - 1}} \cr & = 0 \cr} $$