Simplify (x^2+4x-5)/(x^2+7x-8)*(20x-4x^2)/(x^2+x-30)*(x^2+14x+48)/(x+5)

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 ${\displaystyle 48}$ and whose sum is ${\displaystyle 14}$.

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 ${\displaystyle -5}$ and whose sum is ${\displaystyle 4}$.

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 ${\displaystyle 7}$.

Write the factored form using these integers.

Factor ${\displaystyle 4x}$ out of ${\displaystyle 20x}$.

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

Factor ${\displaystyle 4x}$ out of ${\displaystyle 4x\left(5\right)+4x(-x)}$.

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 ${\displaystyle -30}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x-1}$.

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

Move the negative in front of the fraction.

Rewrite using the commutative property of multiplication.

Multiply ${\displaystyle \frac{4x}{x+6}}$ by ${\displaystyle \frac{x+5}{x+8}}$.

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

Cancel the common factor of ${\displaystyle (x+6)(x+8)}$.