Simplify (3x)/(x-5)*(x^2+4x-45)/(x^2+2x-63)

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 ${\displaystyle -45}$ and whose sum is ${\displaystyle 4}$.

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 ${\displaystyle -63}$ and whose sum is ${\displaystyle 2}$.

Write the factored form using these integers.

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

Combine ${\displaystyle 3}$ and ${\displaystyle \frac{x+9}{(x-7)(x+9)}}$.

Combine ${\displaystyle x}$ and ${\displaystyle \frac{3(x+9)}{(x-7)(x+9)}}$.

Cancel the common factor of ${\displaystyle x+9}$.

Move ${\displaystyle 3}$ to the left of ${\displaystyle x}$.