Simplify (6y)/(y^2-5y+6)*(y^2-3y+2)/(3y-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 ${\displaystyle 6}$ and whose sum is ${\displaystyle -5}$.

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 ${\displaystyle 2}$ and whose sum is ${\displaystyle -3}$.

Write the factored form using these integers.

Factor ${\displaystyle 3}$ out of ${\displaystyle 3y-3}$.

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

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

Multiply ${\displaystyle \frac{2y}{y-3}}$ by ${\displaystyle \frac{y-1}{y-1}}$.

Cancel the common factor of ${\displaystyle y-1}$.