Simplify (x^2-5x-24)/(x^2-9)*(x^2)/(x-8)

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.

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 ${\displaystyle b=3}$.

Cancel the common factor of ${\displaystyle x-8}$.

Combine ${\displaystyle \frac{x+3}{(x+3)(x-3)}}$ and ${\displaystyle x^2}$.

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