Simplify (x^2-x-12)/(x^2-16)*(x^2+2x-8)

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.

Rewrite ${\displaystyle 16}$ as ${\displaystyle 4^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=x}$ and ${\displaystyle b=4}$.

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

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

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.

Cancel the common factor.

Divide ${\displaystyle (x+3)(x-2)}$ by ${\displaystyle 1}$.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Add ${\displaystyle -2x}$ and ${\displaystyle 3x}$.