Simplify (a^2-25)/(a^2+7a+10)

Rewrite ${\displaystyle 25}$ as ${\displaystyle 5^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=a}$ and ${\displaystyle b=5}$.

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 ${\displaystyle 10}$ and whose sum is ${\displaystyle 7}$.

Write the factored form using these integers.

Cancel the common factor.

Rewrite the expression.