Simplify ((x+4)/x)÷((x^2+9x+20)/(x^2+7x+10))

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.

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 ${\displaystyle 9}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x+4}$.

Multiply ${\displaystyle \frac{1}{x}}$ by ${\displaystyle \frac{(x+2)(x+5)}{x+5}}$.

Cancel the common factor of ${\displaystyle x+5}$.