Question

Q:-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

$\huge\tt\underline\blue{Answer }$

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

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

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

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

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

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

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

$⟹\bold{ {x}^{3} - 13 {x}^{2} + 18x - 12}$

$⟹\bold{ {x}^{2} (x - 13) + 6(3x - 2)}$

$⟹\bold{( {x}^{2} + 6)(x - 13)(3x - 2) = 0}$

$⟹ \bold{{x}^{2} + 6 = 0}$

$⟹\bold{\red{x =± \sqrt{6}}}$✓

$⟹\bold{x - 13 = 0}$

$⟹\bold{\red{x = 13}}$✓

$⟹\bold{3x - 2 = 0}$

$⟹\bold{\red{x = \frac{2}{3}}}$✓

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