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Quadratic Equations

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Question

Simplify $\frac{a}{x - a} + \frac{b}{x - b} = \frac{2 c}{x - c}$

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Solution

$\frac{a}{x - a} + \frac{b}{x - b} = \frac{2 c}{x - c}$
$\Rightarrow \frac{a (x - b) + b (x - a)}{(x - a) (x - b)} = \frac{2 c}{(x - c)}$
$\Rightarrow (a x - a b + x b - a b) (x - c) = 2 c (x^{2} - a x - b x + a b)$
$\Rightarrow [(a + b) x - 2 a b] (x - c) = 2 c x^{2} - 2 a c x - 2 b c x + 2 a b x .$

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