Simplify 7/(b^2+5b+4)*(b^2+8b+7)/(b+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 ${\displaystyle 4}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

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 ${\displaystyle 7}$ and whose sum is ${\displaystyle 8}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle b+1}$.

Multiply ${\displaystyle \frac{7}{b+4}}$ by ${\displaystyle \frac{b+7}{b+7}}$.

Cancel the common factor of ${\displaystyle b+7}$.