Simplify (x^3-9x)/(x^2+10x+21)*(x^2+7x)/(x^2+5x-24)

Factor ${\displaystyle x}$ out of ${\displaystyle x^3-9x}$.

Rewrite ${\displaystyle 9}$ as ${\displaystyle 3^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=x}$ and ${\displaystyle b=3}$.

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 ${\displaystyle 21}$ and whose sum is ${\displaystyle 10}$.

Write the factored form using these integers.

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

Factor ${\displaystyle x}$ out of ${\displaystyle 7x}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x\cdot x+x\cdot 7}$.

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.

Cancel the common factor of ${\displaystyle x-3}$.

Cancel the common factor of ${\displaystyle x+7}$.

Multiply ${\displaystyle \frac{x(x+3)}{x+3}}$ by ${\displaystyle \frac{x}{x+8}}$.

Cancel the common factor.

Rewrite the expression.