Solve for x 4/(9x^(2/3))-8/(9x^(5/3))=0

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

Since ${\displaystyle 9x^{\frac{2}{3}},9x^{\frac{5}{3}},1}$ contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 9,9,1}$ then find LCM for the variable part ${\displaystyle x^{\frac{2}{3}},x^{\frac{5}{3}}}$.

The LCM is the smallest positive number that all of the numbers divide into evenly.

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

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

The LCM of ${\displaystyle 9,9,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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

The LCM of ${\displaystyle x^{\frac{2}{3}},x^{\frac{5}{3}}}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

The LCM for ${\displaystyle 9x^{\frac{2}{3}},9x^{\frac{5}{3}},1}$ is the numeric part ${\displaystyle 9}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{4}{9x^{\frac{2}{3}}}-\frac{8}{9x^{\frac{5}{3}}}=0}$ by ${\displaystyle 9x^{\frac{5}{3}}}$.

Simplify the left side.

Simplify the right side.

Add ${\displaystyle 8}$ to both sides of the equation.

Divide each term in ${\displaystyle 4x=8}$ by ${\displaystyle 4}$ and simplify.