Simplify (x^2-9x+20)/(x^2+9x+14)*(x^2+6x+8)/(x^2-x-20)

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.

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 ${\displaystyle 14}$ and whose sum is ${\displaystyle 9}$.

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 ${\displaystyle 8}$ and whose sum is ${\displaystyle 6}$.

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 ${\displaystyle -1}$.

Write the factored form using these integers.

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

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

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

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