Simplify ((c^2-c-20)/(c^2-6c+5))÷((c^2-16)/(3c-3))

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.

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 ${\displaystyle 5}$ and whose sum is ${\displaystyle -6}$.

Write the factored form using these integers.

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

Factor ${\displaystyle 3}$ out of ${\displaystyle 3c-3}$.

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 ${\displaystyle a=c}$ and ${\displaystyle b=4}$.

Cancel the common factor of ${\displaystyle c+4}$.

Cancel the common factor of ${\displaystyle c-1}$.