Find the L.C.M of xto the power of 2 -9 and x to the power of 2+5x+6, explain why and how you got the answer?

Answer 1

First factor the expressions:
x² - 9 = (x - 3)(x + 3)
x² + 5x + 6 = (x + 2)(x + 3)

Next look at the two factorizations. You need an (x - 3) and (x + 3) for the first expression.
For the second one, you already have an (x + 3) so you just need to add an (x + 2). Multiply them all together to get the final answer.

The LCM would be: (x - 3)(x + 3)(x + 2)