Question

Cho biểu thức :

\(A=\left(\frac{x}{x\sqrt{x}-4\sqrt{x}}-\frac{6}{3\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\left(\sqrt{x}-2+\frac{10-x}{\sqrt{x}+2}\right)\)

a) Rút gọn .

b) Tìm x sao cho A < 2 .

Answer 1

a) ĐKXĐ: \(x\ne4\)và \(x>0\)

............................

\(\Leftrightarrow A=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{6}{3\left(\sqrt{x}-2\right)}+\frac{1}{\sqrt{x}+2}\right)\)\(:\left(\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}+2}+\frac{10-x}{\sqrt{x}+2}\right)\)

\(\Leftrightarrow A=\frac{3x-6\sqrt{x}\left(\sqrt{x}+2\right)+3\sqrt{x}\left(\sqrt{x}-2\right)}{3\sqrt{x}\left(\sqrt{x}+2\right)\left(\sqrt{x-2}\right)}:\left(\frac{x-2+10-x}{\sqrt{x}-2}\right)\)

\(\Leftrightarrow A=\frac{3x-6x-12\sqrt{x}+3x-6\sqrt{x}}{3\sqrt{x}\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\left(\frac{8}{\sqrt{x}-2}\right)\)

\(\Leftrightarrow A=\frac{-18\sqrt{x}}{3\sqrt{x}\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\cdot\frac{\sqrt{x}-2}{8}\)

\(\Leftrightarrow A=\frac{-3}{4\left(\sqrt{x}+2\right)}\)

Vậy \(A=\frac{-3}{4\left(\sqrt{x}-2\right)}\)với \(x>0\)và \(x\ne4\)

b)Ta có \(A< 2\Leftrightarrow\frac{-3}{4\left(\sqrt{x}-2\right)}< 2\)

\(\Leftrightarrow\frac{-3}{4\left(\sqrt{x}-2\right)}-2< 0\)

\(\Leftrightarrow\frac{-3-8\left(\sqrt{x}-2\right)}{4\left(\sqrt{x}-2\right)}< 0\)

\(\Leftrightarrow\frac{-3-8\sqrt{x}-16}{4\left(\sqrt{x}-2\right)}< 0\)

\(\Leftrightarrow\frac{-18-8\sqrt{x}}{4\left(\sqrt{x}-2\right)}< 0\)

\(\Leftrightarrow-18-8\sqrt{x}< 0\)( Vì \(4\left(\sqrt{x}-2\right)>0\)với \(\forall x\))

\(\Leftrightarrow\sqrt{x}< \frac{-9}{4}\)(Vô Nghiệm)

Vậy không có gtr nào của x thỏa mãn A<2

Answer 2

Mình làm nhầm bạn ơi, bỏ câu trả lời ý đi nha