Question

$\frac{x - a}{b} = \frac{x - b}{a}$
pls solve this ​

Answer 1

Answer:

$\frac{x - a}{b} = \frac{x - b}{a}$

$a(x -a ) = b(x -b )$

$ax - {a}^{2} =b x - {b}^{2}$

$ax - bx = {a}^{2} - {b}^{2}$

$x(a - b) = {a}^{2} - {b}^{?}$

$x = \frac{ {a}^{2}- {b}^{2} }{a - b}$

Answer 2

$\dfrac{x\: - \:a}{b} \:= \:\dfrac{x\: - \:b}{a}$

_____________ [ GIVEN ]

• We have to simply solve this for x.

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=> $\dfrac{x\: - \:a}{b} \:= \:\dfrac{x\: - \:b}{a}$

Cross multiply them

=> a(x - a) = b(x - b)

=> ax - a² = bx - b²

=> ax - bx = - b² + a²

=> ax - bx = a² - b²

=> x(a - b) = a² - b²

=> x = $\dfrac{ {a}^{2} \: - \: {b}^{2} }{a \: - \: b}$

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

_____________ [ ANSWER ]

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