The L.C.M of $x^{2} - 4$ and $x^{2} - 5 x + 6$ is

(x -2) (x + 2) (x -3)

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(x -2) (x + 2) (x + 3)

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(x + 3) (x -3) (x + 2)

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(x - 2)^{2} (x - 3) (x - 4)

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Solution

The correct option is A (x -2) (x + 2) (x -3)
Since, $x^{2} - 4 = (x^{2} - 2^{2}) = (x + 2) (x - 2)$ [ $∵ a^{2} - b^{2} = (a - b) (a + b)$ ]
and
$x^{2} - 5 x + 6 = x^{2} - 3 x - 2 x - 6$
$= (x - 3) (x - 2)$
$∴$ L.C.M. $= (x - 2) (x + 2) (x - 3)$
Option A is correct.

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