Let a b: - b a = x: y . If ( x - y ) = \ a b + b a \ , then x is equal to -

Answer: Option D

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