(6x+12)/(x+2)^ - (x^-4)/(x-2)^ + x^/x^-4 =0

(6x+12)/(x+2)^=6(x+2)/(x+2)^=6/(x+2)
(x^-4)/(x-2)^=(x-2)(x+2)/(x-2)^=(x+2)/(x-2)
所以,(6x+12)/(x+2)^ - (x^-4)/(x-2)^
=6/(x+2)-(x+2)/(x-2)
通分,=[6(x-2)-(x+2)^]/(x^-4)
=(6x-12-x^-4x-4)/(x^-4)
=(-x^+2x-16)/(x^-4)
所以,(-x^+2x-16)/(x^-4)+x^/(x^-4)=0
(2x-16)/(x^-4)=0
2x-16=0
x=8

解：(6x+12)/(x+2)^ - (x^-4)/(x-2)^ + x^/x^-4 =0
（6x+12）/（x+2）^-(x+2)(x-2)/(x-2)^+x^/(x+2)(x-2)=0
（6x+12）/（x+2）^-(x+2)/(x-2)+x^/(x+2)(x-2)=0
（6x+12）/（x+2）^-(x+2)^/(x-2)(x+2)+x^/(x+2)(x-2)=0

（6x+12）/（x+2）^-<(x+2)^-x^>/(x+2)(x-2)=0
（6x+12）/（x+2）^-2(2x+2)/(x+2)(x-2)=0
（6x+12）/（x+2）^-4(x+1)/(x+2)(x-2)=0
（6x+12）/（x+2）^=4(x+1)/(x+2)(x-2)
（6x+12）/（x+2）^=4(x+1)/(x+2)(x-2)
（6x+12）/（x+2）=4(x+1)/(x-2)
（6x+12）（x-2）=4(x+1)(x+2)
6x^-24=4x^+12x+8
2x^-12x-32=0
x^-6x-16=0
(x-8)(x+2)=0
由原式知：x不能为-