Question 174258
{{{((x)/(x+1))/((1)/(x^2-1) - (1)/(x-1))}}} Start with the given expression.




{{{((x)/(x+1))/((1)/((x+1)(x-1)) - (1)/(x-1))}}} Factor {{{x^2-1}}} to get {{{(x+1)(x-1)}}}



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



{{{((x-1)x)/(1-(x+1))}}} Multiply and simplify



{{{(x(x-1))/(1-(x+1))}}} Rearrange the terms.



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



{{{(x(x-1))/(-x)}}} Combine like terms.



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



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



{{{-x+1}}} Reduce




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



In other words, {{{((x)/(x+1))/((1)/(x^2-1) - (1)/(x-1))=-x+1}}} where {{{x<>-1}}}, {{{x<>0}}}, or {{{x<>1}}}