Simplify ((x^2+4x-32)/(x^2+9x+8))÷((x+7)/(x+1))

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 ${\displaystyle -32}$ and whose sum is ${\displaystyle 4}$.

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 ${\displaystyle 9}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x+1}$.

Multiply ${\displaystyle \frac{(x-4)(x+8)}{x+8}}$ by ${\displaystyle \frac{1}{x+7}}$.

Cancel the common factor of ${\displaystyle x+8}$.