Simplify (x^4-9x^2)/(x^3-3x^2)*(x+5)/(x^2+2x-15)

Factor ${\displaystyle x^2}$ out of ${\displaystyle x^4-9x^2}$.

Rewrite ${\displaystyle 9}$ as ${\displaystyle 3^2}$.

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 ${\displaystyle b=3}$.

Factor ${\displaystyle x^2}$ out of ${\displaystyle x^3}$.

Factor ${\displaystyle x^2}$ out of ${\displaystyle -3x^2}$.

Factor ${\displaystyle x^2}$ out of ${\displaystyle x^{2}x+x^2\cdot -3}$.

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 ${\displaystyle -15}$ and whose sum is ${\displaystyle 2}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle x-3}$.

Multiply ${\displaystyle \frac{x^2(x+3)}{x^2(x-3)}}$ by ${\displaystyle \frac{x+5}{x+5}}$.

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

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