If the equation $\frac{x^{2} - b x}{a x - c}$ $=$ $\frac{m - 1}{m + 1}$ has roots equal in magnitude but opposite in sign, then $m$ is equal to

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Solution

$(x^{2} - b x) (m + 1) = (a x - c) (m - 1)$
Equating the Coeff. of x to zero, we have $- b (m + 1) = a (m - 1)$
$\Rightarrow m = \frac{a - b}{a + b}$

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