Simplify ((x+2)/(x^2+12x+20))÷(1/(x+7))

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 ${\displaystyle 12}$.

Write the factored form using these integers.

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

Multiply ${\displaystyle \frac{1}{x+10}}$ by ${\displaystyle x+7}$.