\(A=\left(\dfrac{x^2-1}{x^2}\right)\left(\dfrac{y^2-1}{y^2}\right)=\dfrac{\left(x-1\right)\left(x+1\right)\left(y-1\right)\left(y+1\right)}{x^2y^2}\)
\(A=\dfrac{-y\left(x+1\right).\left(-x\right)\left(y+1\right)}{x^2y^2}=\dfrac{\left(x+1\right)\left(y+1\right)}{xy}=\dfrac{xy+x+y+1}{xy}\)
\(A=\dfrac{1}{xy}+\dfrac{1}{x}+\dfrac{1}{y}+1\ge\dfrac{4}{\left(x+y\right)^2}+\dfrac{4}{x+y}+1=9\)
\(A_{min}=9\) khi \(x=y=\dfrac{1}{2}\)
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