Find the Roots (Zeros) 3/x=3/(4x)+3

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

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

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

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

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

The LCM of ${\displaystyle 1,4,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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 ${\displaystyle x,4x,1}$ is the numeric part ${\displaystyle 4}$ multiplied by the variable part.

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

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 3+12x=12}$.

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

Divide each term in ${\displaystyle 12x=9}$ by ${\displaystyle 12}$ and simplify.