How do you evaluate #(\frac{1}{x^{2}+1}-\frac{2-x}{x+1})/(\frac{1}{x}+x-2)#?

1 Answer
Manikandan S.
Dec 14, 2017

#((1/(x^2+1) - (2-x)/(x+1)))/(1/x+x-2) = (x/((x^2+1)(x+1))) \times (x+1-(2-x)(x^2+1))/(x^2-2x+1)#
#=x/((x^2+1)(x+1))\times(x^3-2x^2+2x-1)/(x-1)^2#
#= (x\cancel((x-1))(x^2+3x+1))/((x^2+1)(x+1)(x-1)^\cancel(2))#
#=(x^4+3x^2+x)/(x^4-1)#
#=1+(3x^3+x+1)/(x^4-1)#

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