Question

Answer 1

1: \(A=\dfrac{\left(2\sqrt{x}+4\right)\left(\sqrt{x}-1\right)+\sqrt{x}+7-x-4\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{2x-2\sqrt{x}+4\sqrt{x}-4-x-3\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)

\(=\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)

2: Để A<1/6 thì A-1/6<0

\(\Leftrightarrow\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{1}{6}< 0\)

\(\Leftrightarrow6\sqrt{x}-\sqrt{x}-3< 0\)

=>0<=x<9/25