Solve for x 4/(5x)-2/x=3/10

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

Since ${\displaystyle 5x,x,10}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 5,1,10}$ 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.

${\displaystyle 10}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 5}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle 5}$.

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 ${\displaystyle 5x,x,10}$ is the numeric part ${\displaystyle 10}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{4}{5x}-\frac{2}{x}=\frac{3}{10}}$ by ${\displaystyle 10x}$.

Simplify the left side.

Simplify the right side.

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

Divide each term in ${\displaystyle 3x=-12}$ by ${\displaystyle 3}$ and simplify.