a.
Khi \(x=25\Rightarrow A=\dfrac{25+5}{\sqrt{25}-3}=\dfrac{30}{2}=15\)
b.
\(B=\dfrac{2x+4\sqrt{x}-15}{\sqrt{x}\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{2x+4\sqrt{x}-15-\left(x+2\sqrt{x}-15\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{x+2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\)
c.
\(A=\dfrac{A}{B}=\dfrac{x+5}{\sqrt{x}-3}.\dfrac{\sqrt{x}-3}{\sqrt{x}+2}=\dfrac{x+5}{\sqrt{x}+2}\)
\(=\dfrac{x-4+9}{\sqrt{x}+2}=\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)+9}{\sqrt{x}+2}=\sqrt{x}-2+\dfrac{9}{\sqrt{x}+2}\)
\(=\sqrt{x}+2+\dfrac{9}{\sqrt{x}+2}-4\ge2\sqrt{\dfrac{9\left(\sqrt{x}+2\right)}{\sqrt{x}+2}}-4=2\)
\(M_{min}=2\) khi \(x=1\)
