解方程x/(x-1)=1- 3/(1-x)(x+2)

Question

快快
要过程

Answer 1

x/(x-1)=1- 3/(1-x)(x+2)

x/(x - 1) + 3/(1-x)(x+2) -1 = 0
x(x+2) + 3 - (1-x)(x+2)=0
x^2+2x +3 -(x+2-x^2-2x) = 0
2x^2 + 3x + 1 =0
(2x + 1)(x+1) = 0
x = -1 或者 x = -1/2
经过验证x = -1 或者 x = -1/2 不是此方程的解
所以此方程无解

Answer 2

x/(x-1)=1+ 3/(x-1)(x+2)
(x(x+2)-3)/(x-1)=1
(x+3)(x-1)/(x-1)=1
x+3=1
x=-2

Answer 3

x/(x-1)=1- 3/(1-x)(x+2)

x/(x - 1) + 3/(1-x)(x+2) -1 = 0
x(x+2) + 3 - (1-x)(x+2)=0
x^2+2x +3 -(x+2-x^2-2x) = 0
2x^2 + 3x + 1 =0
(2x + 1)(x+1) = 0
x = -1 或者 x = -1/2