Simplify (x/(8x+48))÷((x^2+11x+18)/(x^2+8x+12))

Factor ${\displaystyle 8}$ out of ${\displaystyle 8x}$.

Factor ${\displaystyle 8}$ out of ${\displaystyle 48}$.

Factor ${\displaystyle 8}$ out of ${\displaystyle 8x+8\cdot 6}$.

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 ${\displaystyle 12}$ and whose sum is ${\displaystyle 8}$.

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 ${\displaystyle 18}$ and whose sum is ${\displaystyle 11}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x+6}$.

Multiply ${\displaystyle \frac{x}{8}}$ by ${\displaystyle \frac{x+2}{(x+2)(x+9)}}$.

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