Question

$\frac{1}{(x - 1)(x - 2)} + \frac{1}{(x - 2)(x - 3)} = \frac{2}{3}$
solve will give 13 points

Answer 1

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Answer 2

$\frac{1}{(x - 1)(x - 2)} + \frac{1}{(x - 2)(x - 3)} = \frac{2}{3} \\ \frac{1}{x - 2} - \frac{1}{x - 1} + \frac{1}{x - 3} - \frac{1}{x - 2} = \frac{2}{3} \\ \frac{1}{x - 3} - \frac{1 }{x - 1} = \frac{2}{3} \\ \frac{x - 1 - x + 3}{(x - 3)(x - 1)} = \frac{2}{3} \\ \frac{2}{ {x}^{2} - 4x + 3} = \frac{2}{3} \\ \frac{1}{ {x}^{2} - 4x + 3} = \frac{1}{3} \\ {x}^{2} - 4x + 3 = 3 \\ {x}^{2} - 4x + 3 - 3 = 0 \\ {x}^{2} - 4x = 0 \\ x(x - 4) = 0 \\ x = 0 \: \: \: or \: \: x - 4 = 0 \: \\ x = 4$