Solve the Rational Equation for x 8-6/x=5+12/x

Subtract ${\displaystyle 8}$ from both sides of the equation.

Subtract ${\displaystyle 8}$ from ${\displaystyle 5}$.

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

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

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

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

Multiply each term in ${\displaystyle -\frac{6}{x}=\frac{12}{x}-3}$ by ${\displaystyle x}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 12-3x=-6}$.

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

Divide each term in ${\displaystyle -3x=-18}$ by ${\displaystyle -3}$ and simplify.