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Answer 1 · 2017-10-15T23:45:29

#(x^2+1)/(x-1)^2#

#(x+1+1/x-1)/(x-1+1/x-1)#

The ones cancel each other in the numerator and add in the denominator. Simplify to get:

#(x+1/x)/(x+1/x-2)#

Bring all terms into one fraction with common denominator x.

#(x(x/x)+1/x)/(x(x/x)+1/x-2(x/x))#

Simplifying:

#((x^2+1)/x)/((x^2-2x+1)/x)#

Multiply the numerator by the reciprocal of the denominator to eliminate the complex fraction.

#((x^2+1)/x)*(x/(x^2-2x+1))#

Simplify:

#(x^2+1)/(x-1)^2#