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Mathematics
Problem
Prove that: a.
a
+
b
+
c
a
−
1
b
−
1
+
b
−
1
c
−
1
+
c
−
1
a
−
1
=
a
b
c
\frac{a+b+c}{a^{-1}b^{-1} + b^{-1}c^{-1} + c^{-1}a^{-1}} = abc
a
−
1
b
−
1
+
b
−
1
c
−
1
+
c
−
1
a
−
1
a
+
b
+
c
=
ab
c
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