9: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >4\end{matrix}\right.\)
\(Q=\dfrac{\sqrt{x}-11}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}}{\sqrt{x}+1}+\dfrac{2\sqrt[2]{x}-1}{\sqrt{x}-2}\)
\(=\dfrac{\sqrt{x}-11-\sqrt{x}\left(\sqrt{x}-2\right)+\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}-11-x+2\sqrt{x}+2x+2\sqrt{x}-\sqrt{x}-1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x+4\sqrt{x}-12}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}+6}{\sqrt{x}+1}\)
10:
ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a< >1\end{matrix}\right.\)
a: \(P=\left(\dfrac{1}{a-1}+\dfrac{3\sqrt{a}+5}{\left(a-1\right)\left(\sqrt{a}-1\right)}\right)\cdot\dfrac{a+2\sqrt{a}+1-4\sqrt{a}}{4\sqrt{a}}\)
\(=\dfrac{\sqrt{a}-1+3\sqrt{a}+5}{\left(\sqrt{a}-1\right)^2\cdot\left(\sqrt{a}+1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{4\sqrt{a}}\)
\(=\dfrac{4\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)\cdot4\sqrt{a}}=\dfrac{1}{\sqrt{a}}\)
b: \(Q=\dfrac{a-\sqrt{a}+1}{\sqrt{a}}\)
\(Q-1=\dfrac{a-\sqrt{a}+1-\sqrt{a}}{\sqrt{a}}=\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}}>0\)
=>Q>1
