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Trả lời:
a, \(A=\frac{\sqrt{x}}{\sqrt{x}+3}+\frac{2\sqrt{x}-3}{\sqrt{x}-3}-\frac{2x-\sqrt{x}-3}{x-9}\) \(\left(đkxđ:x\ge0;x\ne9\right)\)
\(=\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{x-9}+\frac{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{x-9}-\frac{2x-\sqrt{x}-3}{x-9}\)
\(=\frac{x-3\sqrt{x}}{x-9}+\frac{2x+3\sqrt{x}-9}{x-9}-\frac{2x-\sqrt{x}-3}{x-9}\)
\(=\frac{x-3\sqrt{x}+2x+3\sqrt{x}-9-2x+\sqrt{x}+3}{x-9}\)
\(=\frac{x+\sqrt{x}-6}{x-9}\)
a) ĐKXĐ: \(x\ge0;x\ne9\)
mk chỉnh lại đề bài nhé, chắc có lẽ bn ghi nhầm:
\(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
\(=\left(\frac{2\sqrt{x}\left(\sqrt{x}-3\right)+\sqrt{x}\left(\sqrt{x}+3\right)-3x-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-\frac{\sqrt{x}-3}{\sqrt{x}-3}\right)\)
\(=\frac{2x-6\sqrt{x}+x+3\sqrt{x}-3x-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}:\frac{2\sqrt{x}-\sqrt{x}+1}{\sqrt{x}-3}\)
\(=\frac{-3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\frac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(=\frac{-3}{\sqrt{x}+3}\)
\(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}+\frac{3x+3}{x-9}\right)\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
\(P=\left[\frac{2\sqrt{x}\left(\sqrt{x}-3\right)}{x-9}+\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{x-9}+\frac{3x+3}{x-9}\right]\) \(\left[\frac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\right]\)
\(P=\frac{2x-6\sqrt{x}+x+3\sqrt{x}+3x+3}{x-9}.\frac{\sqrt{x}+1}{\sqrt{x}-3}\)
\(P=\frac{6x-3\sqrt{x}+3}{x-9}.\frac{\sqrt{x}+1}{\sqrt{x}-3}\)