Question 198378
{{{(1+(1/x))/(1-(1/x^2))}}} Start with the given expression.



{{{(1*x^2+x^(cross(2))(1/cross(x)))/(1*x^2-cross(x^2)(1/cross(x^2)))}}} Multiply EVERY term by the inner LCD {{{x^2}}} to clear out the inner fractions.



{{{(x^2+x)/(x^2-1)}}} Simplify



{{{(x(x+1))/(x^2-1)}}} Factor the numerator



{{{(x(x+1))/((x+1)(x-1))}}} Factor the denominator



{{{(x*cross((x+1)))/(cross((x+1))(x-1))}}} Cancel out the common terms.



{{{x/(x-1)}}} Simplify



So {{{(1+(1/x))/(1-(1/x^2))=x/(x-1)}}}