Simplify (a^2+3a-18)/(a^2-5a+6)*(5a-10)/(a^2-36)

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 ${\displaystyle -18}$ and whose sum is ${\displaystyle 3}$.

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 ${\displaystyle 6}$ and whose sum is ${\displaystyle -5}$.

Write the factored form using these integers.

Factor ${\displaystyle 5}$ out of ${\displaystyle 5a}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle -10}$.

Factor ${\displaystyle 5}$ out of ${\displaystyle 5a+5\cdot -2}$.

Rewrite ${\displaystyle 36}$ as ${\displaystyle 6^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=a}$ and ${\displaystyle b=6}$.

Cancel the common factor of ${\displaystyle a+6}$.

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

Multiply ${\displaystyle \frac{a-3}{a-3}}$ by ${\displaystyle \frac{5}{a-6}}$.

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