Simplify (5x-10)/(x^2-36)*(4x+24)/(x^2+5x-14)

Factor ${\displaystyle 5}$ out of ${\displaystyle 5x}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle -10}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle 5x+5\cdot -2}$.

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

Factor ${\displaystyle 4}$ out of ${\displaystyle 24}$.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4x+4\cdot 6}$.

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 ${\displaystyle -14}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

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

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

Multiply ${\displaystyle \frac{5}{x-6}}$ by ${\displaystyle \frac{4}{x+7}}$.

Multiply ${\displaystyle 5}$ by ${\displaystyle 4}$.