Question

Divide and state any restrictions on the variables.
(x^2-16)/(x^2+5x+6)÷(x^2+5x+4)/(x^2-2x-8)

Answer 1

\[{\frac{x^2-16}{x^2+5x+6}}\div \frac{x^2+5x+4}{x^2-2x-8}\]
Let's first factor the top and the bottom. That's almost always the first step in these types of problems.
\[\frac{(x+4)(x-4)}{(x+3)(x+2)}\div \frac{(x+4)(x+1)}{(x-4)(x+2)}\]
Let's change this to a multiplication problem.
\[\frac{(x+4)(x-4)}{(x+3)(x+2)}\frac{(x-4)(x+2)}{(x+4)(x+1)}\]
Let's start cancelling terms that appear on the top and the bottom. (x+4) and (x+2) will cancel.
\[\frac{(x-4)^2}{(x+3)(x+1)}\]\[x \neq -1,-2,-3, or-4\]