Simplify 3/(x^2-11x+24)*(x^2-64)/(4x+32)*(x^2+6x-27)/(x+9)

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 ${\displaystyle -27}$ 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 ${\displaystyle 24}$ and whose sum is ${\displaystyle -11}$.

Write the factored form using these integers.

Rewrite ${\displaystyle 64}$ as ${\displaystyle 8^2}$.

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 ${\displaystyle b=8}$.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4x+32}$.

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

Multiply ${\displaystyle \frac{3}{x-3}}$ by ${\displaystyle \frac{x+8}{4(x+8)}}$.

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

Multiply ${\displaystyle \frac{3(x+8)}{4(x+8)}}$ by ${\displaystyle \frac{x+9}{x+9}}$.

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

Cancel the common factor of ${\displaystyle x+9}$.