if (a+1/b) varies inversely to (a-1/b) then prove that a varies inversely to b.

If (a+1/b) = 1/ (a-1/b)
or(a+1/b) * (a-1/b) = 1
or (a)2 - (1/b)2 = 1
or a2 = 1+ 1/b2
As 1 is a constant it implies that a2 varies inversely with b2
or a​varies inversely withb

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