Write the Fraction in Simplest Form (w^2-5w-24)/(w+1)*(w^2-6w-7)/(w+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 ${\displaystyle -24}$ and whose sum is ${\displaystyle -5}$.

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 ${\displaystyle -7}$ and whose sum is ${\displaystyle -6}$.

Write the factored form using these integers.

Factor ${\displaystyle w+3}$ out of ${\displaystyle (w-8)(w+3)}$.

Cancel the common factor.

Rewrite the expression.

Factor ${\displaystyle w+1}$ out of ${\displaystyle (w-7)(w+1)}$.

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Subtract ${\displaystyle 8w}$ from ${\displaystyle -7w}$.