Simplify (6x^2-216)/(x^2-2x-48)*(64-x^2)/(x^2+13x+40)*(-x-5)/(x^2-36)

Rewrite ${\displaystyle 36}$ as ${\displaystyle 6^2}$.

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 ${\displaystyle b=6}$.

Factor ${\displaystyle 6}$ out of ${\displaystyle 6x^2-216}$.

Rewrite ${\displaystyle 36}$ as ${\displaystyle 6^2}$.

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 ${\displaystyle b=6}$.

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 ${\displaystyle -48}$ and whose sum is ${\displaystyle -2}$.

Write the factored form using these integers.

Rewrite ${\displaystyle 64}$ as ${\displaystyle 8^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=8}$ and ${\displaystyle b=x}$.

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 ${\displaystyle 40}$ and whose sum is ${\displaystyle 13}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x+6}$.

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

Multiply ${\displaystyle \frac{6(x-6)}{x-8}}$ by ${\displaystyle \frac{8-x}{x+5}}$.

Cancel the common factor of ${\displaystyle x-6}$.

Multiply ${\displaystyle \frac{6(8-x)}{(x-8)(x+5)}}$ by ${\displaystyle \frac{-x-5}{x+6}}$.

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

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

Multiply ${\displaystyle 6}$ by ${\displaystyle -1}$.

Multiply ${\displaystyle -6}$ by ${\displaystyle -1}$.