If x = 4aba + b a b, the value of x + 2ax - 2a + x + 2bx - 2b is?

Answer: Option D

$$\begin{array}{rl}& x=\frac{4ab}{a+b}\\ & \Rightarrow \frac{x}{2a}=\frac{2b}{a+b}\\ & \frac{x+2a}{x-2a}\\ & =\frac{2b+a+b}{2b-a-b}\\ & =\frac{3b+a}{b-a}\end{array}$$
( By Componendo and Dividendo rule )
$$\begin{array}{rl}& \Rightarrow \text{again}\frac{x}{2b}=\frac{2a}{a+b}\\ & \frac{x+2b}{x-2b}\\ & =\frac{2a+a+b}{2a-a-b}\\ & =\frac{3a+b}{a-b}\\ & \Rightarrow \frac{x+2a}{x-2a}\text{ + }\frac{x+2b}{x-2b}\\ & \Rightarrow \frac{3b+a}{b-a}-\frac{3a+b}{a-b}\\ & \Rightarrow \frac{3b+a-3a-b}{b-a}\\ & \Rightarrow \frac{2b-2a}{b-a}\\ & \Rightarrow \frac{2\left(b-a\right)}{\left(b-a\right)}\\ & \Rightarrow 2\end{array}$$