1.a/(b+c)=b/(a+c)=c/(a+b)=k,求k值.2.x/(y+z)=a,y/(z+x)=b,z/(x+y)=c,a/(1+a)+b/(1+b)+c/(1+c)=3.1/(x-2)(x-5)=A/(x-2)+B/(x-5),求A=___,B=___

1.a/(b+c)=b/(a+c)=c/(a+b)=k,求k值.2.x/(y+z)=a,y/(z+x)=b,z/(x+y)=c,a/(1+a)+b/(1+b)+c/(1+c)=3.1/(x-2)(x-5)=A/(x-2)+B/(x-5),求A=___,B=___
1.a/(b+c)=b/(a+c)=c/(a+b)=k,求k值.
2.x/(y+z)=a,y/(z+x)=b,z/(x+y)=c,a/(1+a)+b/(1+b)+c/(1+c)=
3.1/(x-2)(x-5)=A/(x-2)+B/(x-5),求A=___,B=___

1.a/(b+c)=b/(a+c)=c/(a+b)=k,求k值.2.x/(y+z)=a,y/(z+x)=b,z/(x+y)=c,a/(1+a)+b/(1+b)+c/(1+c)=3.1/(x-2)(x-5)=A/(x-2)+B/(x-5),求A=___,B=___
当a+b+c=0时,
b+c=-a
a+c=-b
a+b=-c
这样k=a/-a=b/-b=c/-c=-1
当a+b+c≠0时
把三式相加有
k=(a+b+c)/(2a+2b+2c)=1/2
所以k=-1或1/2
2.先看一部分.
1+a=1+x/(y+z)=(x+y+z)/(y+z)
a/(a+1)=x/(y+z)÷(x+y+z)/(y+z)
=x/(x+y+z)
同理
b/(b+1)=y/(x+y+z)
c/(c+1)=z/(x+y+z)
所以原式=(x+y+z)/(x+y+z)=1
3.两边同乘以(x-2)(x-5)有
1=A(x-5)+B(x-2)
Ax-5A+Bx-2B-1=0
(A+B)x-(5A+2B+1)=0
根据恒等易知
A+B=0
5A+2B+1=0
解得
A=-1/3,B=1/3