1. Cho \(Q=\left(\dfrac{2\sqrt{a}}{\sqrt{a}+3}+\dfrac{\sqrt{a}}{\sqrt{a}-3}-\dfrac{3a+3}{a-9}\right):\left(\dfrac{2\sqrt{a}-2}{\sqrt{a}-3}-1\right)\)
a) Rút gọn Q.
b) Tìm x để \(Q< \dfrac{-1}{2}\)
c) Tìm Qmin
2. \(P=\dfrac{\sqrt{x}+2}{\sqrt{x}+1}-\dfrac{\sqrt{x}+3}{5-\sqrt{x}}-\dfrac{3x+4\sqrt{x}-5}{x-4\sqrt{x}-5}\)
a) Rút gọn P.
b) Tìm x để P > -2
c) Tìm số chính phương x để P có giá trị nguyên.
1.
a. \(Q=\left(\dfrac{2\sqrt{a}}{\sqrt{a}+3}+\dfrac{\sqrt{a}}{\sqrt{a}-3}-\dfrac{3a+3}{a-9}\right):\left(\dfrac{2\sqrt{a}-2}{\sqrt{a}-3}-1\right)=\left(\dfrac{2\sqrt{a}}{\sqrt{a}+3}+\dfrac{\sqrt{a}}{\sqrt{a}-3}-\dfrac{3a+3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}\right):\left(\dfrac{2\sqrt{a}-2-\sqrt{a}+3}{\sqrt{a}-3}\right)=\)
\(\dfrac{2\sqrt{a}\left(\sqrt{a}-3\right)+\sqrt{a}\left(\sqrt{a}+3\right)-3a-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}:\dfrac{\sqrt{a}+1}{\sqrt{a}-3}=\dfrac{2a-6\sqrt{a}+a+3\sqrt{a}-3a-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}.\dfrac{\sqrt{a}-3}{\sqrt{a}+1}=\dfrac{-3\sqrt{a}-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+1\right)}.\dfrac{\sqrt{a}-3}{\sqrt{a}+1}=\dfrac{-3\left(\sqrt{a}+1\right)}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}.\dfrac{\sqrt{a}-3}{\sqrt{a}+1}=-\dfrac{3}{\sqrt{a}+3}\)
Lewther
\(\dfrac{-\sqrt{x}-2}{\sqrt{x}-5}>-2\) (ĐKXĐ: \(x\ge0\) và \(x\ne25\))
\(\Leftrightarrow\dfrac{-\sqrt{x}-2}{\sqrt{x}-5}+2>0\Leftrightarrow\dfrac{-\sqrt{x}-2+2\left(\sqrt{x}-5\right)}{\sqrt{x}-5}>0\Rightarrow-\sqrt{x}-2+2\sqrt{x}-10>0\Leftrightarrow\sqrt{x}-12>0\Leftrightarrow\sqrt{x}>12\Leftrightarrow x>144\)
Vậy ...