Solve for x 4/(3x)+7/x=5/9

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

Since ${\displaystyle 3x,x,9}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 3,1,9}$ 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 ${\displaystyle 3}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 3}$.

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

${\displaystyle 9}$ has factors of ${\displaystyle 3}$ and ${\displaystyle 3}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 3}$.

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 ${\displaystyle 3x,x,9}$ is the numeric part ${\displaystyle 9}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{4}{3x}+\frac{7}{x}=\frac{5}{9}}$ by ${\displaystyle 9x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 5x=75}$.

Divide each term in ${\displaystyle 5x=75}$ by ${\displaystyle 5}$ and simplify.