\(a,A=\dfrac{25+8}{5-1}=\dfrac{33}{4}\\ b,B=\dfrac{x+\sqrt{x}+3\sqrt{x}-3-6\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ B=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\\ c,P=AB=\dfrac{x+8}{\sqrt{x}+1}=\dfrac{x-1+9}{\sqrt{x}+1}=\sqrt{x}+1+\dfrac{9}{\sqrt{x}+1}-2\\ \Leftrightarrow P\ge2\sqrt{9}-2=4\\ P_{min}=4\Leftrightarrow\left(\sqrt{x}+1\right)^2=9\Leftrightarrow\sqrt{x}+1=3\Leftrightarrow x=4\left(tm\right)\)
a) \(A=\dfrac{x+8}{\sqrt{x}-1}=\dfrac{25+8}{\sqrt{25}-1}=\dfrac{33}{4}\)
b) \(B=\dfrac{x+\sqrt{x}+3\sqrt{x}-3-6\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)
