Simplify (x^2-2x-15)/(10x+30)*3/(x^2-3x-10)

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.

Factor ${\displaystyle 10}$ out of ${\displaystyle 10x}$.

Factor ${\displaystyle 10}$ out of ${\displaystyle 30}$.

Factor ${\displaystyle 10}$ out of ${\displaystyle 10x+10\cdot 3}$.

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 ${\displaystyle -10}$ and whose sum is ${\displaystyle -3}$.

Write the factored form using these integers.

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

Multiply ${\displaystyle \frac{x+3}{10(x+3)}}$ by ${\displaystyle \frac{3}{x+2}}$.

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