Question

solve this by quadratic equations
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Answer 1

$\frac{x - a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a} \\ \\ \frac{ {(x - a)}^{2} + {(x - b)}^{2} }{(x - a)(x - b)} = \frac{ {a}^{2} + {b}^{2} }{ab}$

Since (x-a)² is the only term that contains the term a in the numerator and

(x-b)² is the only term that contains the term b in the numerator

we equate LHS to RHS

(x-a)² = a² (x-b)² = b²

x-a = ±a x-b = ±b

x = 2a or 0 x = 2b or 0

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