Simplify ((x^2-100)/(x^2-36)*(9x)/(x+10))÷((5x-10)/(x^2-4x-60))

Rewrite ${\displaystyle 100}$ as ${\displaystyle {10}^2}$.

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 ${\displaystyle b=10}$.

Rewrite ${\displaystyle 36}$ as ${\displaystyle 6^2}$.

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 ${\displaystyle b=6}$.

Cancel the common factor of ${\displaystyle x+10}$.

Combine ${\displaystyle 9}$ and ${\displaystyle \frac{x-10}{(x+6)(x-6)}}$.

Combine ${\displaystyle \frac{9(x-10)}{(x+6)(x-6)}}$ and ${\displaystyle x}$.

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 ${\displaystyle -60}$ and whose sum is ${\displaystyle -4}$.

Write the factored form using these integers.

Factor ${\displaystyle 5}$ out of ${\displaystyle 5x-10}$.

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

Multiply ${\displaystyle \frac{9(x-10)x}{x-6}}$ by ${\displaystyle \frac{x-10}{5(x-2)}}$.