Simplify (x^2-10x+24)/(x^2-x-30)*(x^2-25)/(x^2-16)

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 ${\displaystyle -10}$.

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

Write the factored form using these integers.

Rewrite ${\displaystyle 25}$ as ${\displaystyle 5^2}$.

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 ${\displaystyle b=5}$.

Rewrite ${\displaystyle 16}$ as ${\displaystyle 4^2}$.

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 ${\displaystyle b=4}$.

Cancel the common factor of ${\displaystyle x-4}$.

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

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

Cancel the common factor of ${\displaystyle x-6}$.