Solve for x x/a+x/3=c

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

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

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

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

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.

The LCM of ${\displaystyle 1,3,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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

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

The LCM for ${\displaystyle a,3,1}$ is the numeric part ${\displaystyle 3}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{x}{a}+\frac{x}{3}=c}$ by ${\displaystyle 3a}$.

Simplify the left side.

Simplify the right side.

Factor ${\displaystyle x}$ out of ${\displaystyle 3x+xa}$.

Divide each term in ${\displaystyle x(3+a)=3ca}$ by ${\displaystyle 3+a}$ and simplify.