Question

Solve x+b/a-b = x-b/a+b . Find the value of xv​

Answer 1

Given Equation :

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

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We are here to find the value of x .

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By doing cross multiplication :

${ \dashrightarrow \: \tt \: (a - b)(x - b) = (a + b)(x + b)} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \dashrightarrow \: ax - ab - bx + {b}^{2} = ax + ab + bx + {b}^{2}$

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Cancelling ax and b² from both sides :

$\tt \dashrightarrow \: \cancel{ax} - ab - bx + \cancel{{b}^{2} } = \cancel{ax} + ab + bx + \cancel{ {b}^{2}}$

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Transposing variables on L.H.S and constant terms on R.H.S , we get :

$\tt \dashrightarrow \: - bx - bx = ab + ab \\ \\ \dashrightarrow \tt \: - 2bx = 2ab \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \tt x = - \frac{ \cancel{2}a \cancel{b}}{ \cancel{2} \cancel{b}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \tt \: x = - a \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Henceforth , the value of x is -a .