Simplify (8x-20)/(x^2+2x-35)*(x^2-7x+10)/(4x^2-16)

Factor ${\displaystyle 4}$ out of ${\displaystyle 8x}$.

Factor ${\displaystyle 4}$ out of ${\displaystyle -20}$.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4\left(2x\right)+4(-5)}$.

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 ${\displaystyle -35}$ and whose sum is ${\displaystyle 2}$.

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 ${\displaystyle 10}$ and whose sum is ${\displaystyle -7}$.

Write the factored form using these integers.

Factor ${\displaystyle 4}$ out of ${\displaystyle 4x^2-16}$.

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

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 ${\displaystyle b=2}$.

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

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

Multiply ${\displaystyle \frac{2x-5}{x+7}}$ by ${\displaystyle \frac{x-2}{(x+2)(x-2)}}$.

Cancel the common factor of ${\displaystyle x-2}$.