Solve for x 2+11/(5x)=21/(5x)

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

Since ${\displaystyle 5x,5x,1}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 5,5,1}$ 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.

Since ${\displaystyle 5}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 5}$.

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

The LCM of ${\displaystyle 5,5,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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 ${\displaystyle 5x,5x,1}$ is the numeric part ${\displaystyle 5}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{11}{5x}=\frac{21}{5x}-2}$ by ${\displaystyle 5x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 21-10x=11}$.

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

Divide each term in ${\displaystyle -10x=-10}$ by ${\displaystyle -10}$ and simplify.