Question

方程1/x+2+1/x-2=4/x平方-4的解

Answer 1

两边同乘(x-2)(x+2)得：
x-2+x+2=4
2x=4
x=2
经检验，x=2是方程的增根
所以，原方程无解

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Answer 2

1/(x+2)+1/(x-2)=4/(x+2)(x-2)
都乘以(x+2)(x-2)得，x-2+x+2=4
∴x=2
此时，(x-2)(x+2)=0
∴x=2是增根，原方程无解

Answer 3

1/(x + 2) + 1/(x - 2) = 4/(x" - 4)
1/(x + 2) + 1/(x - 2) - 4/(x + 2)(x - 2) = 0
(x - 2) + (x + 2) - 4 = 0
x - 2 + x + 2 - 4 = 0
2x - 4 = 0
x - 2 = 0
x = 2
可是，分母 x - 2 = 2 - 2 = 0
x = 2 不是原方程的解