Question

If 3x +4y/3u+4v =3x -4y/3u- 4v show that x/y=u/v​

Answer 1

EXPLANATION :

$\sf \LARGE \frac{3x + 4y}{3u + 4v} = \frac{3x - 4y}{3u - 4v} \\ \\ \\ \\ \LARGE \sf \implies \: \frac{3x + 4y}{3x - 4y} = \frac{3u + 4v}{3u - 4v} \\ \\ \\ \\ \LARGE \sf \implies \: \frac{3x + \cancel{4y }+ 3x - \cancel{4y}}{ \cancel{3x} + 4y - \cancel{3x }+ 4y} = \frac{3u + \cancel{4v} + 3u - \cancel{4v}}{ \cancel{3u} + 4v - \cancel{3u} + 4v} \\ \\ \\ \\ \LARGE \sf \implies \: \frac{3x}{4y} = \frac{3u}{4v} \\ \\ \\ \\ \LARGE { \implies} \huge \boxed{\boxed{ \mathfrak{{{ \frac{x}{y} = \frac{u}{v} }}}}} \: \LARGE \bf \: {[Proved]}$

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