Question

已知XY+X/X+Y+1=2 XZ+2X/X+Z+2=3 (Y+1)(Z+2)/Y+Z+3=4 求X+Y+Z的值

已知XY+X/X+Y+1=2 XZ+2X/X+Z+2=3 (Y+1)(Z+2)/Y+Z+3=4 求X+Y+Z的值
已知(XY+X)/(X+Y+1)=2 (XZ+2X)/(X+Z+2)=3 [(Y+1)(Z+2)]/(Y+Z+3)=4 求X+Y+Z的值

Answer 1

(XY+X)/(X+Y+1)=2
(x+y+1)/(xy+x)=1/2
(x+y+1)/x(y+1)=1/2
1/(y+1)+1/x=1/2
同样得：
1/(z+2)+1/x=1/3
1/(y+1)+1/(z+2)=1/4
解方程组得：
1/x=7/24,1/(y+1)=5/24,1/(z+2)=1/24
所以
x=24/7,y=19/5,z=22
x+y+z=29又8/35

Answer 2

XY+X/X+Y+1=2的是（XY+X）/（X+Y+1）=2吗？不是的话就好解了！X/X=1，由XY+X/X+Y+1=2得Y的植，由Y+1)(Z+2)/Y+Z+3=4得Z的植，由XZ+2X/X+Z+2=3得X

Answer 3

d