Solve for x 3/(6x)-9/12=11/(4x)

Add ${\displaystyle \frac{9}{12}}$ to both sides of the equation.

Cancel the common factor of ${\displaystyle 9}$ and ${\displaystyle 12}$.

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

Factor ${\displaystyle 3}$ out of ${\displaystyle 6x}$.

Cancel the common factor.

Rewrite the expression.

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

Since ${\displaystyle 2x,4x,4}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 2,4,4}$ then find LCM for the variable part ${\displaystyle x^1,x^1}$.

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

Since ${\displaystyle 2}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 2}$.

${\displaystyle 4}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 2}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle 2}$.

The factor for ${\displaystyle x^1}$ is ${\displaystyle x}$ itself.

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

The LCM for ${\displaystyle 2x,4x,4}$ is the numeric part ${\displaystyle 4}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{2x}=\frac{11}{4x}+\frac{3}{4}}$ by ${\displaystyle 4x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 11+3x=2}$.

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

Divide each term in ${\displaystyle 3x=-9}$ by ${\displaystyle 3}$ and simplify.