Question

Given $\frac{a}{b}=\frac{c}{d}$, prove that $\frac{3a-5b}{3a+5b}=\frac{3c-5d}{3c+5d}$.

Answer 1

Given $\frac{a}{b}=\frac{c}{d}$

Multiplying both the sides by $\frac{3}{5}$ we get,

$\frac{3a}{5b}=\frac{3c}{5d}$

By componendo-dividendo rule,

We have $\frac{3a-5b}{3a+5b}=\frac{3c-5d}{3c+5d}$

Hence proved.

$\ast$ Componendo-Dividendo Rule:

If $\frac{x}{y}=\frac{p}{q}$ then $\frac{x-y}{x+y}=\frac{p-q}{p+q}$