Simplify (6x-30)/(x^2-7x+10)*(7x-14)/(6x)

Factor ${\displaystyle 6}$ out of ${\displaystyle 6x}$.

Factor ${\displaystyle 6}$ out of ${\displaystyle -30}$.

Factor ${\displaystyle 6}$ out of ${\displaystyle 6x+6\cdot -5}$.

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 ${\displaystyle -7}$.

Write the factored form using these integers.

Factor ${\displaystyle 7}$ out of ${\displaystyle 7x-14}$.

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

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

Multiply ${\displaystyle \frac{x-5}{x-5}}$ by ${\displaystyle \frac{7}{x}}$.

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