Question 174249
This fraction is the numerator: x/x+1
The denominator is: 1/x(exponent 2)-1 MINUS 1/x-1 
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[x/(x+1)] / [1/(x^2-1) - 1/(x-1)]

= [x/(x+1)] / [1 -(x+1)] / (x^2-1)]

= [x/(x+1)] / [-x / (x^2-1)]

Invert the denominator and multiply :

= [x/(x+1)] / [(x^2-1) /-x ]

Cancel where you can to get:

= [1/1] / [(x-1)/(-1)]

= (x-1)/(-1)

= 1-x 
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Cheers,
Stan H.