> 数学 >
若x+y+z≠0,a=
x
y+z
,b=
y
x+z
,c=
z
x+y
,则
a
a+1
+
b
b+1
+
c
c+1
=(  )
A. 0
B. 1
C. a+b+c
D. 不确定
人气:368 ℃ 时间:2020-10-02 02:16:21
解答
∵x+y+z≠0,把a=
x
y+z
,b=
y
x+z
,c=
z
x+y
代入得
a
a+1
+
b
b+1
+
c
c+1

=
x
x+y+z
+
y
x+y+z
+
z
x+y+z

=
x+y+z
x+y+z
=1.
故选B.
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