Simplify 1/(p-9)*(p^2+6p-27)/(p+9)

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 ${\displaystyle -27}$ and whose sum is ${\displaystyle 6}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle p+9}$.

Multiply ${\displaystyle \frac{1}{p-9}}$ by ${\displaystyle p-3}$.