解下列分式方程:
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/16 06:03:14
解下列分式方程:
![解下列分式方程:](/uploads/image/z/20011009-49-9.jpg?t=%E8%A7%A3%E4%B8%8B%E5%88%97%E5%88%86%E5%BC%8F%E6%96%B9%E7%A8%8B%EF%BC%9A)
/>x/(y+z)=y/(x+z+1)=z/(x+y-1)=x+y+z
(x+y+z)/(2x+2y+2z-1+1)=x+y+z(比例的性质)
(x+y+z)/[2(x+y+z)]=x+y+z
1/2=x+y+z
于是
x/(y+z)=y/(x+z+1)=z/(x+y-1)=1/2
2x=y+x
2y=x+z+1
2z=x+y-1
解三元一次方程即可
再问: 帮忙解出来
再答: x/(y+z)=y/(x+z+1)=z/(x+y-1)=x+y+z (x+y+z)/(2x+2y+2z-1+1)=x+y+z(比例的性质) (x+y+z)/[2(x+y+z)]=x+y+z 1/2=x+y+z 于是 x/(y+z)=y/(x+z+1)=z/(x+y-1)=x+y+z=1/2 于是 x/(y+z)=1/2即x/(1/2-x)=1/2 解得x=1/6 y/(x+z+1)=1/2即y/(1/2-y+1)=1/2 解得y=1/2 z=1/2-y-x=1/2-1/2-1/6=-1/6 所以原方程的解为 x=1/6 y=1/2 z=-1/6
(x+y+z)/(2x+2y+2z-1+1)=x+y+z(比例的性质)
(x+y+z)/[2(x+y+z)]=x+y+z
1/2=x+y+z
于是
x/(y+z)=y/(x+z+1)=z/(x+y-1)=1/2
2x=y+x
2y=x+z+1
2z=x+y-1
解三元一次方程即可
再问: 帮忙解出来
再答: x/(y+z)=y/(x+z+1)=z/(x+y-1)=x+y+z (x+y+z)/(2x+2y+2z-1+1)=x+y+z(比例的性质) (x+y+z)/[2(x+y+z)]=x+y+z 1/2=x+y+z 于是 x/(y+z)=y/(x+z+1)=z/(x+y-1)=x+y+z=1/2 于是 x/(y+z)=1/2即x/(1/2-x)=1/2 解得x=1/6 y/(x+z+1)=1/2即y/(1/2-y+1)=1/2 解得y=1/2 z=1/2-y-x=1/2-1/2-1/6=-1/6 所以原方程的解为 x=1/6 y=1/2 z=-1/6