Simplify (x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40)

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 ${\displaystyle b=4}$.

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 ${\displaystyle -90}$ and whose sum is ${\displaystyle 1}$.

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 ${\displaystyle 40}$ and whose sum is ${\displaystyle 14}$.

Write the factored form using these integers.

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

Simplify terms.

Rewrite ${\displaystyle -1x}$ as ${\displaystyle -x}$.