giúp tớ bài 7 ạa
a.
\(P=\left(\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{x-1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}-\dfrac{x-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\right)\)
\(=\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}{3}\)
\(=\dfrac{\sqrt{x}-2}{3\sqrt{x}}\)
b.
\(P< \dfrac{1}{4}\Rightarrow\dfrac{\sqrt{x}-2}{3\sqrt{x}}< \dfrac{1}{4}\)
\(\Rightarrow4\left(\sqrt{x}-2\right)< 3\sqrt{x}\) (do \(\sqrt{x}>0;\forall x\in TXĐ\))
\(\Rightarrow4\sqrt{x}-8< 3\sqrt{x}\)
\(\Rightarrow\sqrt{x}< 8\)
\(\Rightarrow x< 64\)
Kết hợp ĐKXĐ \(\Rightarrow\left\{{}\begin{matrix}0< x< 64\\x\ne1;x\ne4\end{matrix}\right.\)
c.
\(P>\dfrac{1}{6}\Rightarrow\dfrac{\sqrt{x}-2}{3\sqrt{x}}>\dfrac{1}{6}\)
\(\Rightarrow6\left(\sqrt{x}-2\right)>3\sqrt{x}\) (do \(\sqrt{x}>0;\forall x\in TXĐ\))
\(\Rightarrow3\sqrt{x}>12\)
\(\Rightarrow\sqrt{x}>4\)
\(\Rightarrow x>16\)
