Question

1/x-3 + 2/x-2 =8/x????
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Answer 1

$\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x} \\ \\ = > \frac{x - 2 + 2x - 6}{(x - 3)(x - 2)} = \frac{8}{x} \\ \\ = > \frac{ {x}^{2} - 2x - 3x + 6 }{3x - 8} = \frac{x}{8} \\ \\ = > \frac{ {x}^{2} - 5x + 6 }{3x - 8} = \frac{x}{8} \\ \\ = > 8 {x}^{2} - 40x + 48 = 3 {x}^{2} - 8x \\ \\ = > 5 {x}^{2} - 32x + 48 = 0 \\ \\ = > 5 {x}^{2} - 20x - 12x + 48 = 0 \\ \\ = > 5x(x - 4) - 12(x - 4) = 0 \\ \\ = > (x - 4)(5x - 12) = 0 \\ \\ Required \: valves \: of \: x \: = 4 \: and \: \frac{12}{5}$

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