Rút gọn biểu thức: P=√x/√x+3−3/√x−3+6√x/x−9 (với x≥0,x≠9).

\(P=\frac{\sqrt[]{x}}{\sqrt[]{x}+3}-\frac{3}{\sqrt[]{x}-3}+\frac{6\sqrt[]{x}}{x-9}\)

=\(\frac{\sqrt[]{x}}{\sqrt[]{x}+3}-\frac{3}{\sqrt[]{x}-3}+\frac{6\sqrt[]{x}}{\left. \sqrt[]{x}-3 \right..(\sqrt[]{x}+3)}\)

=\(\frac{\sqrt[]{x}\left. \sqrt[]{x}-3 \right.-3\left. \sqrt[]{x}+3 \right.+6\sqrt[]{x}}{\left. \sqrt[]{x}-3 \right..(\sqrt[]{x}+3)}\)

= \(\frac{x-3\sqrt[]{x}-3\sqrt[]{x}-9+6\sqrt[]{x}}{\left. \sqrt[]{x}-3 \right..(\sqrt[]{x}+3)}\) = \(\frac{x-9}{\left. \sqrt[]{x}-3 \right..(\sqrt[]{x}+3)}\) = 1

Vậy P=1