Simplify ((x^2+5x+6)/(2x+4)*(x+8)/(x+2))÷((x^2+11x+24)/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 ${\displaystyle 5}$.

Write the factored form using these integers.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2x+4}$.

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

Multiply ${\displaystyle \frac{x+3}{2(x+2)}}$ by ${\displaystyle x+8}$.

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 ${\displaystyle 24}$ and whose sum is ${\displaystyle 11}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle (x+3)(x+8)}$.

Combine ${\displaystyle \frac{1}{2(x+2)}}$ and ${\displaystyle 3}$.