Simplify (x+5)/(9x+27)*(x^2-9)/(x^2+2x-15)

Factor ${\displaystyle 9}$ out of ${\displaystyle 9x}$.

Factor ${\displaystyle 9}$ out of ${\displaystyle 27}$.

Factor ${\displaystyle 9}$ out of ${\displaystyle 9x+9\cdot 3}$.

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 ${\displaystyle b=3}$.

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 ${\displaystyle x+5}$.

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

Multiply ${\displaystyle \frac{1}{9}}$ by ${\displaystyle \frac{x-3}{x-3}}$.

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