\(P=\frac{\left(x^2-1\right)\left(y^2-1\right)}{x^2y^2}=\frac{\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)}{x^2y^2}=\frac{xy\left(x+1\right)\left(y+1\right)}{x^2y^2}=\frac{\left(x+1\right)\left(y+1\right)}{xy}\)
\(P=\frac{xy+x+y+1}{xy}=1+\frac{1}{x}+\frac{1}{y}+\frac{1}{xy}\)
\(P\ge1+\frac{4}{x+y}+\frac{4}{\left(x+y\right)^2}=9\)
\(P_{min}=9\) khi \(x=y=\frac{1}{2}\)