Question

find lcm of x^2-1 and x^2-x-2

Answer 1

$x {}^{2} - 1 \\ = (x + 1)(x - 1)$

and

$x {}^{2} - x {}^{ - 2} \\ = x {}^{2} - \frac{1}{x {}^{2} } \\ = \frac{x {}^{4} - 1 }{x {}^{2} } \\ = \frac{1}{x {}^{2} } (x {}^{2} - 1)(x {}^{2} + 1) \\ = \frac{1}{x {}^{2} } (x - 1)(x + 1)(x {}^{2} + 1)$

now the LCM is

$\frac{1}{x {}^{2} } (x - 1)(x + 1)(x {}^{2} + 1)$