Simplify (x^2)/(4x+8)*(x^2-4)/(x^2+6x-16)

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

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

Factor ${\displaystyle 4}$ out of ${\displaystyle 4x+4\cdot 2}$.

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 ${\displaystyle b=2}$.

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 ${\displaystyle -16}$ and whose sum is ${\displaystyle 6}$.

Write the factored form using these integers.

Combine.

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

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