(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)=

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(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)=
(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)=

(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)=
=[(3x^2+9x+7)(x-1)-(2x^2+4x-3)(x+1)-(x^3+x+1)]/(x^2-1)=(4x+5)/(1-x^2)