a, ĐKXĐ: \(x\ge0;x\ne1;x\ne\frac{1}{4}\)
\(P=\left[\frac{2x\sqrt{x}+x-\sqrt{x}}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}-\frac{\sqrt{x}.\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}\right].\frac{\left(\sqrt{x}-1\right).\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right).\left(2\sqrt{x}-1\right)}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(=\frac{2x\sqrt{x}+x-\sqrt{x}-\sqrt{x}.\left(x+\sqrt{x}+1\right)}{\left(x+\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(=\frac{\sqrt{x}\left(x-2\right)}{\left(x+\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
\(=\frac{\sqrt{x}\left(x-2\right)+\sqrt{x}\left(x+\sqrt{x}+1\right)}{\left(x+\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}=\frac{\sqrt{x}\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(x+\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}=\frac{x+\sqrt{x}}{x+\sqrt{x}+1}\)
b, \(P=\frac{x+\sqrt{x}}{x+\sqrt{x}+1}=\frac{x+\sqrt{x}+1-1}{x+\sqrt{x}+1}=1-\frac{1}{x+\sqrt{x}+1}\ge1-\frac{1}{1}=0\)
\(MinP=0\Leftrightarrow x=0\)
