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

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 .
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 .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Subtract from .
Combine the numerators over the common denominator.
Simplify the numerator.
Subtract from .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Reduce the expression by cancelling the common factors.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
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 .
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 .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Subtract from .
Combine the numerators over the common denominator.
Simplify the numerator.
Subtract from .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Reduce the expression by cancelling the common factors.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Since , there are no solutions.
No solution
Solve by Factoring x/(x-1)-1/(x+1)=2/(x^2-1)