Simplify (x^2+2x-15)/(x^2+5x-24)*(4x+32)/(x+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 ${\displaystyle -15}$ 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 ${\displaystyle -24}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4x+32}$.

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

Multiply ${\displaystyle \frac{(x-3)(x+5)}{x-3}}$ by ${\displaystyle \frac{4}{x+4}}$.

Cancel the common factor of ${\displaystyle x-3}$.

Move ${\displaystyle 4}$ to the left of ${\displaystyle x+5}$.