If x/y = a + 2a - 2 , then the value of x^2 - y^2x^2 + y^2 = ?

Answer: Option B

$$\begin{array}{rl}& \frac{x}{y}\text{ = }\frac{a+2}{a-2}\\ & \frac{x^2}{y^2}\text{ = }\frac{{\left(a+2\right)}^2}{{\left(a-2\right)}^2}\end{array}$$
Applying componendo and dividendo
$$\begin{array}{rl}& \therefore \frac{x^2-y^2}{x^2+y^2}\\ & =\frac{{\left(a+2\right)}^2-{\left(a-2\right)}^2}{{\left(a+2\right)}^2+{\left(a-2\right)}^2}\\ & =\frac{8a}{2a^2+8}\\ & =\frac{4a}{a^2+4}\end{array}$$