x/(xy+x＋1)＋y/(yz+y+1)＋z/(xz+z+1)=?其中 xyz＝1

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/18 01:13:23

结果等于：1
原式=x/(xy+x+xyz)＋y/(yz+y+xyz)＋z/(xz+z+xyz)
=1/(y+1+yz)+1/(z+1+xz)+1/(x+1+xy)
=xyz/(y+xyz+yz)+1/(z+1+xz)+1/(x+1+xy)
=xz/(1+xz+z)+1/(z+1+xz)+1/(x+1+xy)
=(xz+1)/(z+1+xz)+1/(x+1+xy)
=(xz+xyz)/(z+xyz+xz)+1/(x+1+xy)
=(x+xy)/(1+xy+x)+1/(x+1+xy)
=1

x/(xy+x＋1)＋y/(yz+y+1)＋z/(xz+z+1)=?其中 xyz＝1 XYZ-XY-XZ+X-YZ+Y+Z-1 xyz-xy-xz+x-yz+y+z-1因式分解设x,y,z∈R+,xy+yz+xz=1,证明不等式:(xy)^2/z+(xz)^2/y+(yz)^2/x+6xyz≥x xy／x+y＝1,yz／y＋z＝2,xz／x＋z＝3求x,y 已知xyz=1,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值已知,xyz=0,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1）值? x+y+z=1,x,y,z都是正数,求xy+yz+xz-3xyz的最大值和最小值 xy/x+y=1 yz/y+z=2 xz/x+z=3 求xyz/x+y+z=? 已知x+y+z=3,xy+yz+xz=-1,xyz=2,求x^2y^2+y^2z^2+x^2z^2 X,Y,Z为实数,且XY/X+Y=1/3,YZ/Y+Z=1/4,XZ/X+Z=1/5,求XYZ/XY+YZ+XZ的值证明当x+y+z=1时,x/yz+y/xz+z/xy≥9