# Solve the Rational Equation for x 1/(x-1)-1=x/(x-1)

Solve the Rational Equation for x 1/(x-1)-1=x/(x-1)
Add to both sides of the equation.
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Multiply each term in by to eliminate the fractions.
Multiply each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Solve the equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.