解方程：（1）2/x=3/x+1 (2)1/x-4=8/x^2-16 化简：(12/m^2-9)+(2/3-m)

(1)令1/x=t ,即改为 2t=3t+1
则t+1=0,所以t=1/x= -1,即x=-1 .
(2)令1/x=t ,即改为 t-4=8t^2-16
化简为 8t^2-t-12=0
求出t=-1/16±√385/16=1/x,
求出x=16/(-1±√385)
以后类似的题目均可以利用此法先求出其倒数的值,再求其值

1.2x+2=3x
x=2
2.1/(x-4)=1/(x+4)(x-4)
x+4=1
x=-3
3.12/(m+3)(m-3)-2/(m-3)
=[12-2(m+3)]/(m+3)(m-3)
=-2/(m+3)

（1）2/x=3/(x+1)
2(x+1)=3x
2x+2=3x
x=2
(2)1/(x-4)=8/(x^2-16)
8(x-4)=x^2-16=(x+4)(x-4)
(x-4)(x+4-8)=0
(x-4)^2=0
x-4=0
x=4
带入检验,x=4使得分母x-4和x^2-16等于0
不成立
所以原方程无解
12/(m^2-9)+2/(3-m)
=12/(m^2-9)-2/(m-3)
=12/(m^2-9)-2(m+3)/(m-3)(m+3)
=(12-2m-6)/(m-3)(m+3)
=(6-2m)/(m-3)(m+3)
=2(m-3)/(m-3)(m+3)
=2/(m+3)