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Simplify: 1/(1+(log)a b c)+1/(1+(log)b c...

Simplify: `1/(1+(log)_a b c)+1/(1+(log)_b c a)+1/(1+(log)_c a b)`

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`(1)/(1+log_(a)bc)+(1)/(1+log_(b)ca)+(1)/(1+log_(c)ab)`
`=(1)/(1+(logbc)/(loga))+(1)/((1+logca)/(logb))+(1)/(1+(logab)/(loga))`
`=(loga)/(loga+logb+logc)+(logb)/(loga+log+logc)+(logc)/(loga+log+logc)`
=1
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