Simplify (x^2-36)/(x^2-3x-18)*(2x+6)/(x+6)

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 ${\displaystyle -18}$ and whose sum is ${\displaystyle -3}$.

Write the factored form using these integers.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2x+6}$.

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

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

Combine ${\displaystyle \frac{x-6}{x-6}}$ and ${\displaystyle 2}$.

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