If $x = \frac{5ab}{a - b}$, a ≠ b,

(a) Given,

$x = \frac{5ab}{a - b}$

Multiplying $\frac{1}{a}$ on both sides of equation :

$$\begin{aligned}\Rightarrow \frac{x}{a} = \frac{1}{a} \Big(\frac{5ab}{a - b}\Big) \\[1em] \Rightarrow \frac{x}{a} = \frac{5b}{a - b}.\end{aligned}$$

Hence, $\frac{x}{a} = \frac{5b}{a - b}.$

(b) Since,

$\frac{x}{a} = \frac{5b}{a - b}$

Applying componendo and dividendo, we get :

$$\begin{aligned}\Rightarrow \frac{x + a}{x - a} = \frac{5b + (a - b)}{5b - (a - b)} \\[1em] \Rightarrow \frac{x + a}{x - a} = \frac{a + 4b}{6b - a}.\end{aligned}$$

Hence, $\frac{x + a}{x - a} = \frac{a + 4b}{6b - a}.$