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

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Vedantu Content Team · Accepted Answer

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 $\dfrac{{a + b}}{{a - b}} = \dfrac{{c + d}}{{c - d}}$ Complete step-by-step answer:Given, $\dfrac{a}{b} = \dfrac{c}{d}$ 			equation (1)$\dfrac{e}{f} = \dfrac{g}{h}$ 			equation (2)Multiplying both the equation (1) and (2)$\dfrac{{ae}}{{bf}} = \dfrac{{cg}}{{dh}}$ By dividendo and componendo$\dfrac{{ae + bf}}{{ae - bf}} = \dfrac{{cg + dh}}{{cg - dh}}$ 
NOTE: Whenever you come to this type of problem first convert the given form to a rational form that multiplies both the equation and after applying the dividendo and componendo get the final answer.

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

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

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