If a = xx + y and b = yx - y , then aba + b is equal to = ?

Answer: Option A

$$\begin{array}{rl}& \frac{ab}{a+b}=\frac{\frac{x}{x+y}\times \frac{y}{x-y}}{\frac{x}{x+y}+\frac{y}{x-y}}\\ & \frac{ab}{a+b}=\frac{\frac{xy}{x^2-y^2}}{\frac{x\left(x-y\right)+y\left(x+y\right)}{x^2-y^2}}\\ & \frac{ab}{a+b}=\frac{xy}{x^2+y^2}\end{array}$$