Question

# If a : b = c : d and e : f = g : h, prove that ae + bf : ae – bf = cg + dh : cg –dh

Hint: Here we have to multiply both the equations by dividendo and componendo.
As per this rule, if $\dfrac{a}{b} = \dfrac{c}{d}$,
Then this can be expressed as $\dfrac{{a + b}}{{a - b}} = \dfrac{{c + d}}{{c - d}}$

Given, $\dfrac{a}{b} = \dfrac{c}{d}$ equation (1)
$\dfrac{e}{f} = \dfrac{g}{h}$ equation (2)
$\dfrac{{ae}}{{bf}} = \dfrac{{cg}}{{dh}}$
$\dfrac{{ae + bf}}{{ae - bf}} = \dfrac{{cg + dh}}{{cg - dh}}$