\(P=\frac{2}{\sqrt{x}-1}+\frac{2\left(\sqrt{x}+1\right)}{x+\sqrt{x}+1}+\frac{x-10\sqrt{x}+3}{\sqrt{x^3}-1}\)
\(=\frac{2\left(x+\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)+x-10\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{2x+2\sqrt{x}+2+2x-2+x-10\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{5x-8\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\left(\sqrt{x}-1\right)\left(5\sqrt{x}-3\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{5\sqrt{x}-3}{x+\sqrt{x}+1}\)
Với \(x\ge0;x\ne1\), ta có:
\(P=\frac{2}{\sqrt{x}-1}+\frac{2.\left(\sqrt{x}+1\right)}{x+\sqrt{x}+1}+\frac{x-10\sqrt{x}+3}{\sqrt{x^3}-1}\)
\(P=\frac{2.\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}+\frac{2.\left(\sqrt{x}+1\right).\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}+\frac{x-10\sqrt{x}+3}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{2x+2\sqrt{x}+2+2.\left(x-1\right)+x-10\sqrt{x}+3}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{3x-8\sqrt{x}+5+2x-2}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{5x-\sqrt{8x}+3}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{5x-5\sqrt{x}-3\sqrt{x}+3}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}\)
\(P=\frac{\left(\sqrt{x}-1\right).\left(5\sqrt{x}-3\right)}{\left(\sqrt{x}-1\right).\left(x+\sqrt{x}+1\right)}=\frac{5\sqrt{x}-3}{x+\sqrt{x}+1}\)
Vậy với \(x\ge0;x\ne1\) ta có: \(P=\frac{5\sqrt{x}-3}{x+\sqrt{x}+1}\)