a) \(U=\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(U=\dfrac{15\sqrt{x}-11}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\dfrac{3\sqrt{x}-2}{\sqrt{x}-1}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(U=\dfrac{15\sqrt{x}-11-\left(3\sqrt{x}-2\right)\left(\sqrt{x}+3\right)-\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(U=\dfrac{15\sqrt{x}-11-\left(3x+9\sqrt{x}-2\sqrt{x}-6\right)-\left(2x-2\sqrt{x}+3\sqrt{x}-3\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(U=\dfrac{15\sqrt{x}-11-3x-9\sqrt{x}+2\sqrt{x}+6-2x+2\sqrt{x}-3\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(U=\dfrac{-5x+7\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\Leftrightarrow\dfrac{-5\left(\sqrt{x}-1\right)\left(\sqrt{x}-\dfrac{2}{5}\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(\Leftrightarrow\dfrac{-5\left(\sqrt{x}+\dfrac{2}{5}\right)}{\sqrt{x}+3}\Leftrightarrow\dfrac{-5\sqrt{x}-2}{\sqrt{x}+3}\)
b) ta có \(U=\dfrac{1}{2}\) \(\Leftrightarrow\dfrac{-5\sqrt{x}-2}{\sqrt{x}+3}=\dfrac{1}{2}\) \(\Leftrightarrow\sqrt{x}+3=2\left(-5\sqrt{x}-2\right)\)
\(\Leftrightarrow\sqrt{x}+3=-10\sqrt{x}-4\Leftrightarrow\sqrt{x}+3-\left(-10\sqrt{x}-4\right)\)
\(\Leftrightarrow\sqrt{x}+3+10\sqrt{x}+4=0\Leftrightarrow11\sqrt{x}+7=0\Leftrightarrow11\sqrt{x}=-7\)
\(\Leftrightarrow\sqrt{x}=\dfrac{-7}{11}\left(vôlí\right)\)
vậy không có giá trị nào để \(U=\dfrac{1}{2}\)
