Question

解方程：x/x+2-x+2/x-2=8/x平方-4

X+2分之x减去x-2分之x+2=x平方-4分之8

Answer 1

x/(x+2)-(x+2)/(x-2)=8/(x^2-4)
显然x≠-2, 2
去分母得x(x-2)-(x+2)^2=8
6x=-12
x=-2 (与已知矛盾，舍去)
所以原方程无解

Answer 2

x/x+2-x+2/x-2=8/x平方-4
(x/x+2)-(x+2/x-2)-(8/x平方-4)=0
[x(x-2)-(x+2)(x+2)-8]/(x平方-4)=0
(-6x-12)/(x平方-4)=0
-6x-12=0且x平方-4不等于0
x无解

Answer 3

两边乘(x+2)(x-2)
x(x-2)-(x+2)平方=8
x平方-2x-x平方-4x-4=8
6x=-12
x=-2
经检验，x=-2，分母x+2=0，是增根，舍去
方程无解

Answer 4

x/(x+2)-(x+2)/(x-2)=8/(x平方-4)
x/(x+2)-(x+2)/(x-2)-8/{(x+2)(x-2)}=0
{ x(x-2)-(x+2)(x-2)-8} / {(x+2)(x-2)} = 0
{ x^2-2x-x^2+4-8} / {(x+2)(x-2)} = 0
{ -2x-4} / {(x+2)(x-2)} = 0
-2(x+2) / {(x+2)(x-2)} = 0
-2 / (x-2) = 0
无解

Answer 5

可以把题目再写清楚吗？题目有歧义