Simplify (x^2+x-6)/((x^2-4)(x+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 ${\displaystyle -6}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

Rewrite ${\displaystyle 4}$ as ${\displaystyle 2^2}$.

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 ${\displaystyle b=2}$.

Cancel the common factor of ${\displaystyle x-2}$.

Cancel the common factor of ${\displaystyle x+3}$.