Simplify (x^2+3x-18)/(x^2-36)

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 ${\displaystyle -18}$ and whose sum is ${\displaystyle 3}$.

Write the factored form using these integers.

Rewrite ${\displaystyle 36}$ as ${\displaystyle 6^2}$.

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 ${\displaystyle b=6}$.

Cancel the common factor.

Rewrite the expression.