Solve for y 6/(3y-18)-3=2/(y-6)

Factor ${\displaystyle 3}$ out of ${\displaystyle 3y-18}$.

Reduce the expression ${\displaystyle \frac{6}{3(y-6)}}$ by cancelling the common factors.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number ${\displaystyle 1}$ is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of ${\displaystyle 1,1,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

The factor for ${\displaystyle y-6}$ is ${\displaystyle y-6}$ itself.

${\displaystyle (y-6)}$ occurs ${\displaystyle 1}$ time.

The LCM of ${\displaystyle y-6,y-6}$ is the result of multiplying all factors the greatest number of times they occur in either term.

Multiply each term in ${\displaystyle \frac{2}{y-6}=\frac{2}{y-6}+3}$ by ${\displaystyle y-6}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 3y-16=2}$.

Move all terms not containing ${\displaystyle y}$ to the right side of the equation.

Divide each term in ${\displaystyle 3y=18}$ by ${\displaystyle 3}$ and simplify.