Question

If a : b = c : d, prove that: (9a + 13b)(9c – 13d) = (9c + 13d)(9a – 13b).

Answer 1

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

${\displaystyle \Rightarrow \frac{9a}{13b}=\frac{9c}{13d}}$  ...${\displaystyle \left(\text{Multiplying each side by}\frac{9}{13}\right)}$

${\displaystyle \Rightarrow \frac{9a+13b}{9a-13b}=\frac{9c+13d}{9c-13d}}$   ...(By componendo and divdendo)

${\displaystyle \Rightarrow (9a+13b)(9c-13d)=(9c+13d)(9a-13b)}$