Simplify ((x^2-x-12)/(4x+12))÷((x^2-6x+8)/6)

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 ${\displaystyle 4}$ out of ${\displaystyle 4x+12}$.

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

Multiply ${\displaystyle \frac{(x-4)(x+3)}{2(x+3)}}$ by ${\displaystyle \frac{3}{x^2-6x+8}}$.

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 ${\displaystyle 8}$ and whose sum is ${\displaystyle -6}$.

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.