Solve the Rational Equation for x 3/x-1/3=1/6

Add ${\displaystyle \frac{1}{3}}$ to both sides of the equation.

To write ${\displaystyle \frac{1}{3}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{2}{2}}$.

Write each expression with a common denominator of ${\displaystyle 6}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Add ${\displaystyle 1}$ and ${\displaystyle 2}$.

Cancel the common factor of ${\displaystyle 3}$ and ${\displaystyle 6}$.

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

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

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 ${\displaystyle 2}$ has no factors besides ${\displaystyle 1}$ and ${\displaystyle 2}$.

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

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

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

The LCM for ${\displaystyle x,2}$ is the numeric part ${\displaystyle 2}$ multiplied by the variable part.

Multiply each term in ${\displaystyle \frac{3}{x}=\frac{1}{2}}$ by ${\displaystyle 2x}$.

Simplify the left side.

Simplify the right side.