Simplify (a^2+a-20)/(36a-9a^2)

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 ${\displaystyle 9a}$ out of ${\displaystyle 36a-9a^2}$.

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

Move the negative in front of the fraction.