三元方程组(x+y+1)/(xy+x)=1/2(x+z+2)/(xz+2x)=1/3(y+z+3)/(y+1)(z+2)=1/4

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三元方程组(x+y+1)/(xy+x)=1/2(x+z+2)/(xz+2x)=1/3(y+z+3)/(y+1)(z+2)=1/4
三元方程组
(x+y+1)/(xy+x)=1/2
(x+z+2)/(xz+2x)=1/3
(y+z+3)/(y+1)(z+2)=1/4

三元方程组(x+y+1)/(xy+x)=1/2(x+z+2)/(xz+2x)=1/3(y+z+3)/(y+1)(z+2)=1/4
设a=x,b=y+1,c=z+2,则方程组化为:
(a+b)/ab=1/2
(a+c)/ac=1/3
(b+c)/bc=1/4
即:
1/a+1/b=1/2
1/a+1/c=1/3
1/b+1/c=1/4
所以,
1/a+1/b+1/c=(1/2+1/3+1/4)/2=13/24
1/a=13/24-1/4=7/24
1/b=13/24-1/3=5/24
1/c=13/24-1/2=1/24
所以,
x=a=24/7
y+1=b=24/5,y=19/5
z+2=c=24,z=22
x=24/7,y=19/5,z=22