Question

解下列方程：2/x-1-3/x+1=x+3/x²-1;6x-2/2x-1-6x-3/3x-1=1.

最好有详细计算过程

Answer 1

2/(x-1)-3/(x+1)=(x+3)/(x²-1)
2(x+1)/(x-1)(x+1)-3(x-1)/(x+1)(x-1)=(x+3)/(x²-1)
(2x+2)/(x²-1)-(3x-3)/(x²-1)=(x+3)/(x²-1)
(2x+2)/(x²-1)-(3x-3)/(x²-1)-(x+3)/(x²-1)=0
(2x+2-3x+3-x-3)/(x²-1)=0
(2-2x)/(x²-1)=0
-2(x-1)/(x+1)(x-1)=0
2/(x+1)=0
x无解

(6x-2)/(2x-1)-(6x-3)/(3x-1)=1
2(3x-1)/(2x-1)-3(2x-1)/(3x-1)=1
2(3x-1)²/(2x-1)(3x-1)-3(2x-1)²/(2x-1)(3x-1)=1
2(3x-1)²--3(2x-1)²=(2x-1)(3x-1)
2(9x²-6x+1)-3(4x²-4x+1)=(6x²-5x+1)
6x²-1=6x²-5x+1
5x=2
x=0.4
经检验，x=0.4是原方程的解