$\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}$ .

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Solution

$\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6} \Rightarrow \frac{(x - 3) + (x - 1)}{(x - 1) (x - 1) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}$
$\frac{2 (x - 2) +}{(x - 1) (x - 3) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6} \Rightarrow \frac{2 (x - 4) + (x - 1)}{(x - 1) (x - 3) (x - 4)} = \frac{1}{6}$
$\frac{3 (x - 3)}{(x - 1) (x - 3) (x - 4)} = \frac{1}{6} \Rightarrow \frac{3}{(x - 1) (x - 4)} = \frac{1}{6}$
$18 = x^{2} - 5 x + 4 \Rightarrow x^{2} - 5 x + 14 = 0 \Rightarrow (x - 7) (x + 2) = 0$
$x 7, - 2$

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Similar questions

Q. Evaluate

[\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)}] = \frac{1}{6}

Q. Solve for

x : \frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}

Q. Solve for x, 1÷(x-1)(x-2)+1÷(x-2)(x-3)+1÷(x-3)(x-4)=1÷6

Solve the following quadratic equation by factorization.
$\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}$

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

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1(x−1)(x−2)+1(x−2)(x−3)+1(x−3)(x−4)=16.

$\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}$ .