Simplify ((x^2-x-20)/(2x+10))÷((x^2-16)/(x^2+x-20))

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 ${\displaystyle -20}$ and whose sum is ${\displaystyle -1}$.

Write the factored form using these integers.

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

Factor ${\displaystyle 2}$ out of ${\displaystyle 10}$.

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

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 ${\displaystyle -20}$ 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 ${\displaystyle x+4}$.

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

Multiply ${\displaystyle \frac{x-5}{2}}$ by ${\displaystyle \frac{x-4}{x-4}}$.

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