问题 填空题
已知:
ab
a+b
=
1
24
bc
b+c
=
1
36
ac
a+c
=
1
44
,则
abc
ab+bc+ca
=______.
答案

ab
a+b
=
1
24
bc
b+c
=
1
36
ac
a+c
=
1
44

a+b
ab
=24,
b+c
bc
=36,
a+c
ac
=44,

1
a
+
1
b
=24,

1
b
+
1
c
=36,

1
c
+
1
a
=44,

∴2(

1
a
+
1
b
+
1
c
)=104,

1
a
+
1
b
+
1
c
=52,

ab+bc+ac
abc
=
1
a
+
1
b
+
1
c
=52,

abc
ab+bc+ca
=
1
52

故答案为:

1
52

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