Simplify ((x^2-x-12)/(3x+9))÷((x^2+x-20)/(x+5))

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.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3x+9}$.

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

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 ${\displaystyle -20}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

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

Multiply ${\displaystyle \frac{1}{3}}$ by ${\displaystyle \frac{x+5}{x+5}}$.

Cancel the common factor of ${\displaystyle x+5}$.