Question

解方程:2/(x-1)-3/(x+1)=(x+3)/(x^2-1)

快。过程要全

Answer 1

2/(x-1)-3/(x+1)=(x+3)/(x^2-1)
2(x+1)/[(x-1)(x+1)]-3(x-1)/[(x+1)(x-1)]=(x+3)/(x^2-1)
[2(x+1)-3(x-1)]/[(x+1)(x-1)]=(x+3)/(x^2-1)
[2(x+1)-3(x-1)]/(x^2-1)=(x+3)/(x^2-1)
2x+2-3x+3=x+3
x=1
因为（x-1）=0，0不能是分母，所以这个方程无解。
也就是x=1为此方程的增根。

Answer 2

x/(x-1)=1+3/(x^2+x-2)
方程两边同时乘以x²+x-2,得
则x(x+2)=x²+x-2+3
则x²+2x=x²+x+1
则x=1
检验：将x=1代入原方程，分母=0，所以x=1是增根
所以原方程无解。

Answer 3

2/(x-1)-3/(x+1)=(x+3)/(x^2-1)
2(x+1)-3(x-1)=(x+3)
2x+2-3x+3=x+3
2x=2
x=1
2/(x-1)-3/(x+1)=(x+3)/(x^2-1)
x^2-1≠0，x≠±1
x=1为增根

Answer 4

解：由2/(x-1)-3/(x+1)=(x+3)/(x^2-1)得
2（x+1）-3(x-1)=x+3(x不等于-1和1)
解得x=1,所以，方程无解