Question

5/x-2+1/x-1=6/x,where x not equal to 0,1,2

Answer 1

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Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2

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$⟹ \frac{5}{x - 2} + \frac{1}{x - 1} = \frac{6}{x}$

$⟹ \frac{5(x - 1) + x - 2}{(x - 1)(x - 2)} = \frac{6}{x}$

$⟹ \frac{5x - 5 + x - 2}{(x - 2)(x - 1)} = \frac{6}{x}$

$⟹ \frac{6x - 7}{(x - 2)(x - 1)} = \frac{6}{x}$

$⟹ \frac{x(6x - 7)}{x(x - 1) - 2(x - 1)} = \frac{6}{x}$

$⟹ \frac{ {x}^{2} - 7x}{ {x}^{2} - x - 2x + 2} = \frac{6}{x}$

$⟹ {x}^{3} - 7 {x}^{2} = 6 {x}^{2} - 18x + 12$

$⟹ {x}^{3} - 13 {x}^{2} + 18x - 12$

$⟹ {x}^{2} (x - 13) + 6(3x - 2)$

$⟹( {x}^{2} + 6)(x - 13)(3x - 2) = 0$

$⟹ {x}^{2} + 6 = 0$

$⟹x =± \sqrt{6}$✓

$⟹x - 13 = 0$

$⟹x = 13$✓

$⟹3x - 2 = 0$

$⟹x = \frac{2}{3}$✓

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Answer 2

Answer:

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