Simplify (x^2-2x-8)/(x^2+3x+2)*(4x+4)/(x^2-x-12)

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 ${\displaystyle 2}$ and whose sum is ${\displaystyle 3}$.

Write the factored form using these integers.

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

Factor ${\displaystyle 4}$ out of ${\displaystyle 4}$.

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

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 ${\displaystyle -12}$ and whose sum is ${\displaystyle -1}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x-4}$.

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

Multiply ${\displaystyle \frac{x+2}{x+2}}$ by ${\displaystyle \frac{4}{x+3}}$.

Cancel the common factor of ${\displaystyle x+2}$.