可化为一元二次方程的分式方程

令x=2k+1
y=3k-1
z=4k+2
代入1/x+1/y+1/z=1得 k=1
x=3
y=2
z=6

假设(x-1)/2=(y+1)/3=(z-2)/4=k
x=2k+1
y=3k-1
z=4k+2
代入到
1/x+1/y+1/z=1
可以求出k

解：设(x-1)/2=(y+1)/3=(z-2)/4=T
则X=2T+1,Y=3T-1,Z=4T+2
1/x+1/y+1/z=1/(2T+1)+1/(3T-1)+1/(4T+2)=1
即 3/(4T+2）+1/(3T-1)=1
得 T=-1/12或T=1
T=-1/12时，X=2T+1=5/6,Y=3T-1=-5/4,Z=4T+2=5/3
T=1时，X=2T+1=3,Y=3T-1=2,Z=4T+2=6