Question

solve: 1/(x-1)(x-2) + 1/(x-2)(x-3) = 2/3

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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