If pqr=1, then prove that [ 1/(1+p+q^{-1})] + [1/(1+q+r^{-1})] + [1/(1+r+p^{-1})] = 1

pqr = 1

r = 1/pq

1/r = pq

(1/1+p+q^{-1}) + (1/1+q+r^{-1}) + (1/1+r+p^{-1})

(1/(1+p+1/q) + (1/(1+q+pq) + (1/(1+1/pq+1/p)

(1/(q+pq+1/q) + (1/(q+pq+1) + (1/(q+pq+1/pq)

(q/q+pq+1) + (1/q+pq+1) + (pq/q+pq+1)

(q+pq+1) / (q+pq+1)

= 1

hence proved

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