Inequality ((ab-1)(bc-1)(ca-1))/((a^2-1)(b^2-1)(c^2-1))

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Numerical experiments indicate that the inequality 1 < [tex]\frac{(ab-1)(bc-1)(ca-1)}{(a^{2 }-1)( b^{2 }-1)( c^{2 }-1)}[/tex] < [tex]\frac{9}{8}[/tex] appears to be true when [tex]3 \le a < b < c[/tex].

Is there an easy proof? Or is it a hard Olympiad type problem?