Solve for x 1/(5x)+(x+4)/x=6/5

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

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

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

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

Multiply each term in ${\displaystyle \frac{1}{5x}+\frac{x+4}{x}=\frac{6}{5}}$ by ${\displaystyle 5x}$.

Simplify the left side.

Simplify the right side.

Move all terms containing ${\displaystyle x}$ to the left side of the equation.

Subtract ${\displaystyle 21}$ from both sides of the equation.

Divide each term in ${\displaystyle -x=-21}$ by ${\displaystyle -1}$ and simplify.