Question

Solve : x+a/x-a=b-a/b+a​

Answer 1

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{x + a}{x - a} = \dfrac{b - a}{b + a}$

We know,

If a : b : : c : d, then

$\boxed{\tt{ \frac{a + b}{a - b} = \frac{c + d}{c - d} \: is \: called \: componendo \: and \: dividendo }}$

So, On applying Componendo and Dividendo, we get

$\rm :\longmapsto\:\dfrac{x + a + x - a}{x + a - (x - a)} = \dfrac{b - a + b + a}{b - a - (b + a)}$

$\rm :\longmapsto\:\dfrac{2x}{x + a - x + a} = \dfrac{2b}{b - a - b - a}$

$\rm :\longmapsto\:\dfrac{2x}{2a} = \dfrac{2b}{ - 2a}$

$\bf\implies \:x = \: - \: b$

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Explore more

If a : b : : c : d, then

$\boxed{\tt{ \frac{a}{c} = \frac{b}{d} \: is \: called \:alternendo}}$

$\boxed{\tt{ \frac{b}{a} = \frac{d}{c} \: is \: called \:invertendo}}$

$\boxed{\tt{ \frac{a - b}{b} = \frac{c - d}{d} \: is \: called \:dividendo}}$

$\boxed{\tt{ \frac{a + b}{b} = \frac{c + d}{d} \: is \: called \:componendo}}$

Answer 2

$\huge \color{navy}\maltese \bold \color{red} \: answer$