Use the product property of logarithms, .

Use the quotient property of logarithms, .

Multiply and .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor.

Rewrite the expression.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify/Condense natural log of x/(x-1)+ natural log of (x+1)/x- natural log of x^2-1