Question

3/x-1 - 1/x-3 = 2/x-2

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$\frac{3}{ x - 1} - \frac{1}{x - 3} = \frac{2}{x - 2} \\ \\ \\ = > \frac{3(x - 3) - (x - 1)}{(x - 1)(x - 3)} = \frac{2}{x - 2} \\ \\ \\ \\ \\ = > \frac{3x - 9 - x + 1}{(x - 1)(x - 3)} = \frac{2}{x - 2} \\ \\ \\ \\ = > \frac{2x - 8}{ {x}^{2} - 3x - x + 3 } = \frac{2}{x - 2} \\ \\ = \\ \\ \\ \\ = > \frac{x - 4}{ {x}^{2} - 4x + 3} = \frac{1}{x - 2} \\ \\ \\ \\ = > (x - 4)(x - 2) = {x}^{2} - 4x + 3 \\ \\ = > {x}^{2} - 2x - 4x + 8 = {x}^{2} - 4x + 3 \\ \\ \\ = > - 6x + 8 = - 4x + 3 \\ \\ \\ \\ = > 8 - 3 = - 4x + 6x \\ \\ \\ = > 5 = 2x \\ \\ = > x = \frac{5}{2}$

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