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\(B=\frac{3\sqrt{x}+1}{x+2\sqrt{x}-3}-\frac{2}{\sqrt{x}+3}\) ĐK : \(x\ge0;x\ne1\)
\(=\frac{3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{2}{\sqrt{x}+3}\)
\(=\frac{3\sqrt{x}+1-2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{1}{\sqrt{x}-1}\)
\(=\frac{3\sqrt{x}+1}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}-\frac{2}{\sqrt{x}+3}\)
\(=\frac{3\sqrt{x}+1-2\cdot\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}\)
\(=\frac{3\sqrt{x}+1-2\sqrt{x}+2}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}\)
\(=\frac{\sqrt{x}+3}{\left(\sqrt{x}+3\right)\cdot\left(\sqrt{x}-1\right)}\)
\(=\frac{1}{\sqrt{x}-1}\)
\(B=\frac{3\sqrt{x}+1}{x+2\sqrt{x}-3}-\frac{2}{\sqrt{x}+3}\)
\(=\frac{3\sqrt{x}+1-2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{3\sqrt{x}+1-2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\frac{1}{\sqrt{x}-1}\)
\(x^2-x+1\)
\(=\left(2+\sqrt3\right)^2-\left(2+\sqrt3\right)+1\)
\(=7+4\sqrt3-2-\sqrt3+1=6+3\sqrt3\)
\(\left(x-1\right)\cdot\sqrt3\)
\(=\left(2+\sqrt3-1\right)\cdot\sqrt3=\sqrt3\left(\sqrt3+1\right)\)
\(\frac{\left(x-1\right)\cdot\sqrt3}{\sqrt{x^2-x+1}}\)
\(=\frac{\sqrt3\left(\sqrt3+1\right)}{6+3\sqrt3}=\frac{\sqrt3\left(\sqrt3+1\right)}{3\left(2+\sqrt3\right)}=\frac{1}{\sqrt3}\cdot\frac{\sqrt3+1}{2+\sqrt3}\)
\(=\frac{1}{\sqrt3}\cdot\frac{2\left(\sqrt3+1\right)}{4+2\sqrt3}\)
\(=\frac{1}{\sqrt3}\cdot\frac{2\left(\sqrt3+1\right)}{\left(\sqrt3+1\right)^2}=\frac{1}{\sqrt3}\cdot\frac{2}{\sqrt3+1}=\frac{2}{3+\sqrt3}\)
\(=\frac{2\left(3-\sqrt3\right)}{9-3}=\frac{2\left(3-\sqrt3\right)}{6}=\frac{3-\sqrt3}{3}\)
\(\left(3\sqrt{7}\right)^2=63>28=\left(\sqrt{28}\right)^2\) hoặc \(3\sqrt{7}>2\sqrt{7}=\sqrt{28}\)