(3x^2+9x+7)/(x+1)-(2x^2+4x-3)/(x-1)-(x^3+x+1)/(x^2-1)=SORRY打错了(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)=SORRY打错了(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)=
SORRY打错了
(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)=SORRY打错了(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）/（x^2-1）-（2x^2+4x-3）(x-1)/（x^2-1）-（x^3+x+1)/(x^2-1)
=（3x^3+12x^2+16x+7）/（x^2-1）-（2x^3+2x^2-7x+3）/（x^2-1）-（x^3+x+1)/(x^2-1）
=（10x^2+22x+3）/(x^2-1）

第一项上下同乘（x-1）
第二项上下同乘（x+1）
计算得（-4x-5)/(x^2-1)
乘完一共15项懒得打上来，你自己算算就出来了
（10x^2+22x+3)/(x^2-1)

(3x^2+9x+7)/(x-1)-(2x^2+4x-3)/(x+1)-(x^3+x+1)/(x^2-1)
通分得
=(3x^2+9x+7)(x+1)/(x-1)(x+1)-(2x^2+4x-3)(x-1)/(x+1)(x-1)-(x^3+x+1)/(x^2-1)
=(3x^3+12x^2+16x+7)/(x^2-1)- (2x^3+2x^2-7x+3)/(x^2-1)-(x^3+x+1)/(x^2-1)
=(3x^3+12x^2+16x+7-2x^3-2x^2+7x-2-x^3-x-1)/(x^2-1)
=(10x^2+22x+4)/(x^2-1)

(3x^2+9x+7)/(x-1)-(2x^2+4x-3)/(x+1)-(x^3+x+1)/(x^2-1)
=(3x²+9x+7)(x+1)/(x²-1)-(2x²+4x-3)(x+1)/(x²-1)-(x³+x+1)/(x²-1)
=(3x³+9x²+7x+3x²+9x+7-2x³-2x²-4x²-4x+3x+3-x³-x-1)/(x²-1)
=(6x²+14x+9)/(x²-1)