Simplify ((x^2-9x+20)/(x-5))÷((x^2-16)/(x^2+4x))

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 ${\displaystyle -9}$.

Write the factored form using these integers.

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

Factor ${\displaystyle x}$ out of ${\displaystyle x^2+4x}$.

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 ${\displaystyle x+4}$.