Divide ((x^2-16)/(x^2+5x+6))/((x^2+5x+4)/(x^2-2x-8))

Rewrite ${\displaystyle 16}$ as ${\displaystyle 4^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=x}$ and ${\displaystyle b=4}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 6}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -8}$ and whose sum is ${\displaystyle -2}$.

Write the factored form using these integers.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 4}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Factor ${\displaystyle x+4}$ out of ${\displaystyle (x+1)(x+4)}$.

Cancel the common factor.

Rewrite the expression.

Factor ${\displaystyle x+2}$ out of ${\displaystyle (x-4)(x+2)}$.

Cancel the common factor.

Rewrite the expression.