Find the Product (x^2+5x-36)/(x^2-49)*(x^2-11x+28)

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 ${\displaystyle -36}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Rewrite ${\displaystyle 49}$ as ${\displaystyle 7^2}$.

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 ${\displaystyle b=7}$.

Factor ${\displaystyle x^2-11x+28}$ using the AC method.

Combine exponents.

Cancel the common factor.

Rewrite the expression.