If a : b = c : d, prove that :

5a + 7b : 5a - 7b = 5c + 7d : 5c - 7d

Given,

⇒ a : b = c : d

$\therefore \dfrac{a}{b} = \dfrac{c}{d} \\[1em]$

Multiplying both sides by $\dfrac{5}{7}$:

$\Rightarrow \dfrac{5a}{7b} = \dfrac{5c}{7d}$

Applying componendo and dividendo:

$\Rightarrow \dfrac{5a + 7b}{5a - 7b} = \dfrac{5c + 7d}{5c - 7d}$

Hence, proved that 5a + 7b : 5a - 7b = 5c + 7d : 5c - 7d.