Question 156667
{{{x/(x^2-1)  + 1/(x-1)  = 1/(x+1)}}} Start with the given equation



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



{{{(x-1)(x+1)(x/(cross((x-1)(x+1)))  + 1/cross(x-1))  = 1/cross(x+1)}}} Multiply both sides by the LCD {{{(x-1)(x+1)}}} to clear out the fractions.



{{{x+x+1=x-1}}} Distribute and multiply



{{{2x+1=x-1}}} Combine like terms on the left side.



{{{2x=x-1-1}}} Subtract {{{1}}} from both sides.



{{{2x-x=-1-1}}} Subtract {{{x}}} from both sides.



{{{x=-1-1}}} Combine like terms on the left side.



{{{x=-2}}} Combine like terms on the right side.



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Answer:


So the answer is {{{x=-2}}}