Solve for a 1/(3a^2)-1/a=1/(6a^2)

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

Since ${\displaystyle 3a^2,a,6a^2}$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part ${\displaystyle 3,1,6}$ then find LCM for the variable part ${\displaystyle a^2,a^1,a^2}$.

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.

${\displaystyle 6}$ has factors of ${\displaystyle 2}$ and ${\displaystyle 3}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle 3}$.

The factors for ${\displaystyle a^2}$ are ${\displaystyle a\cdot a}$, which is ${\displaystyle a}$ multiplied by each other ${\displaystyle 2}$ times.

The factor for ${\displaystyle a^1}$ is ${\displaystyle a}$ itself.

The factors for ${\displaystyle a^2}$ are ${\displaystyle a\cdot a}$, which is ${\displaystyle a}$ multiplied by each other ${\displaystyle 2}$ times.

The LCM of ${\displaystyle a^2,a^1,a^2}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

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

The LCM for ${\displaystyle 3a^2,a,6a^2}$ is the numeric part ${\displaystyle 6}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{1}{3a^2}-\frac{1}{a}=\frac{1}{6a^2}}$ by ${\displaystyle 6a^2}$.

Simplify the left side.

Simplify the right side.

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

Divide each term in ${\displaystyle -6a=-1}$ by ${\displaystyle -6}$ and simplify.