Question

1) 1/(x - 1)(x - 2) + 1/(x - 2)(x - 4) + 1/(x - 3)(x - 4) = 1/6 where, x not equal to 1,2,3,4.
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Answer 1

Answer:

➻ $\dfrac{1}{(x - 2)} - \dfrac{1}{(x - 1)} + \dfrac{1}{(x - 3)} - \dfrac{1}{(x - 2)} + \dfrac{1}{(x - 4)} - \dfrac{1}{(x - 3)} =\: \dfrac{1}{6}$

➻ $\dfrac{1}{x - 4} - \dfrac{1}{x - 1} =\: \dfrac{1}{6}$

➻ $\dfrac{x -1 - x + 4}{(x -4) (x - 1)} =\: \dfrac{1}{6}$

➻ $\dfrac{3}{(x - 4) (x - 1)} =\: \dfrac{1}{6}$

➻ $\dfrac{3}{{x}^{2} - 5x + 4} =\: \dfrac{1}{6}$

➻ ${x}^{2} - 5x + 4 =\: 18$

➻ ${x}^{2} - 5x + 4 - 18 =\: 0$

➻ ${x}^{2} - 5x - 14 =\: 0$

➻ ${x}^{2} - 7x + 2x - 14 =\: 0$

➻ $x (x - 7) +2(x -7) = 0$

➻ $(x -7) (x + 2) = 0$

➻ $x - 7 = 0 , x + 2 = 0$

➻ $x = 7 , x = - 2$

➠ $x = 7, - 2$