Question

1/(x-1) (x-2)+1/(x-2) (x-3) = 2/3​

Answer 1

$\mathbb{\huge{\pink{\underline{\underline{\underline{\underline{solution}}}}}}}$

$\frac{1}{(x - 1)(x - 2)} + \frac{1}{(x - 2)(x - 3)} = \frac{2}{3} \\ \\ \frac{1}{(x - 2)} ( \: \frac{1}{x - 1} + \frac{1}{x - 3} ) \\ \\ \frac{1}{(x - 2)} ( \frac{x - 3 + x - 1}{(x - 1)(x - 3)}) \\ \\ \frac{1}{(x - 2)} ( \frac{2x - 4}{ {x}^{2} - 3x - x \: + 3} ) \\ \\ \frac{1}{(x - 2)} ( \frac{2x - 4}{ {x}^{2} \: - 4x + 3 } ) \\ \\ \frac{1}{(x - 2)} ( \frac{2(x - 2)}{ {x}^{2} - 4x + 3 } ) \\ \\ now \: ( x- 2) \: will \: get \: cancelled . \\ \\ \frac{2}{ {x}^{2} - 4x + 3 } =\frac{2}{3} \\ \\ 2\: will \: get \: cancelled \\ \\ 3 = {x}^{2} - 4x + 3 \\ \\ {x}^{2} - 4x = 0 \\ \\ {x}^{2} = 4x \\ \\ </p><p>x = -+ 2root{x}</p><p></p><p></p><p></p><p>$

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