ĐKXĐ: \(x>0;a\ne1\)
\(P=\left(\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}-\dfrac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}+1\right)}\right):\dfrac{\sqrt{a}+1}{a}\)
\(=\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right):\dfrac{\sqrt{a}+1}{a}=\left(\dfrac{a-1}{\sqrt{a}}\right).\left(\dfrac{a}{\sqrt{a}+1}\right)\)
\(=\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right).a}{\sqrt{a}\left(\sqrt{a}+1\right)}=\sqrt{a}\left(\sqrt{a}-1\right)\)
\(=a-\sqrt{a}\)
\(P=a-\sqrt{a}+\dfrac{1}{4}-\dfrac{1}{4}=\left(\sqrt{a}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)
\(P_{min}=-\dfrac{1}{4}\) khi \(a=\dfrac{1}{4}\)
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