a) \(P=\left(\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+3}{x-9}\right):\left(\dfrac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
- ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne9\end{matrix}\right.\)
\(P\Leftrightarrow\left(\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{x-9}+\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{x-9}-\dfrac{3x-3}{x-9}\right):\left(\dfrac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\right)\)\(\Leftrightarrow\dfrac{2x-6+x+3\sqrt{x}-3x-3}{x-9}.\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\Leftrightarrow\dfrac{3\sqrt{x}-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\Leftrightarrow\dfrac{3\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\sqrt{x-3}}{\sqrt{x}+1}\)
\(\Leftrightarrow\dfrac{3}{\sqrt{x}+1}\)
b)\(P< \dfrac{-1}{3}\Leftrightarrow\dfrac{3}{\sqrt{x}+1}< -\dfrac{1}{3}\)
\(\Leftrightarrow-\dfrac{1}{3}-\dfrac{3}{\sqrt{x}+1}>0\)
\(\Leftrightarrow-\left(\dfrac{1}{3}+\dfrac{3}{\sqrt{x}+1}\right)>0\) (Sai)
\(\Rightarrow\)Không có giá trị nào của \(x\) để \(P< -\dfrac{1}{3}\)
c) \(P=\dfrac{3}{\sqrt{x}+1}\)Chỉ xđ đc GTLN là 3 mình nghĩ vậy!
Thông cảm!
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