已知1=xy/(x+y),2=yz/(y+z),3=xz/(x+z),求x+y+z的值.已知A/(x+3)+B/(x-1)=2/[(x+3)(x-1)],求A、B的值.若x/3=y/5=z/7,求(x-y+z)/y的值.(2-x):x=x:(1-x),则x等于多少

Question

已知1=xy/(x+y),2=yz/(y+z),3=xz/(x+z),求x+y+z的值.
已知A/(x+3)+B/(x-1)=2/[(x+3)(x-1)],求A、B的值.
若x/3=y/5=z/7,求(x-y+z)/y的值.
(2-x):x=x:(1-x),则x等于多少

Answer 1

三个已知全部取倒数,得
(x+y)/xy=1
1/x+1/y=1.①
(y+z)/yz=1/2
1/y+1/z=1/2.②
(x+z)/xz=1/3
1/x+1/z=1/3.③
①、②、③,解得：x=2.4,y=12/7,z=-12
x+y+z=2.4+12/7-12=-276/35
已知A/(x+3)+B/(x-1)=2/[(x+3)(x-1)],求A、B的值.
[A(x-1)+B(x+3)]/(x-1)(x+3)=2/(x+3)(x-1)
[(A+B)x+(-A+3B)]/(x+3)(x-1)=2/(x+3)(x-1)
A+B=0
-A+3B=2
B=1/2
A=-1/2
若x/3=y/5=z/7,求(x-y+z)/y的值.
设：x/3=y/5=z/7=k
则有：x=3k,y=5k,z=7k
(x-y+z)/y=(3k-5k+7k)/5k=1
(2-x):x=x:(1-x),则x等于多少
x^2=(2-x)(1-x)
x^2=x^2-3x+2
3x=2
x=2/3