# Solve by Factoring 2/(x^2-1)-1/(x-1)=1

Move to the left side of the equation by subtracting it from both sides.
Simplify .
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Cancel the common factor of and .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Reorder and .
Rewrite as .
Factor out of .
Move the negative in front of the fraction.
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Subtract from .
Cancel the common factor of and .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Factor out of .
Reorder and .
Rewrite as .
Factor out of .
Move the negative in front of the fraction.
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 by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Multiply by .
Solve the equation.
Add to both sides of the equation.
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
Solve by Factoring 2/(x^2-1)-1/(x-1)=1