If $a : b = c : d$ , and $e : f = g : h$ , prove that $a e + b f : a e - b f = c g + d h : c g - d h$ .

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Solution

Given , $\frac{a}{b} = \frac{c}{d}, \frac{e}{f} = \frac{g}{h}$

multiplying both the equations,

$\frac{a e}{b f} = \frac{c g}{d h}$

By dividendo and componendo

$\frac{a e + b f}{a e - b f} = \frac{c g + d h}{c g - d h}$

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