Question

a) Rút gọn (x>0, x khác 1)

b) Tìm giá trị x để p<0

Answer 1

\(a,=\left(\dfrac{x-1}{2\sqrt{x}}\right)^2\cdot\dfrac{x-2\sqrt{x}+1-x-2\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ =\dfrac{\left(\sqrt{x}-1\right)^2\left(\sqrt{x}+1\right)^2}{4x}\cdot\dfrac{-4\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ =\dfrac{\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)}{\sqrt{x}}\)

\(b,P< 0\Leftrightarrow\dfrac{\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)}{\sqrt{x}}< 0\\ \Leftrightarrow\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)< 0\left(\sqrt{x}>0\right)\\ \Leftrightarrow1-\sqrt{x}< 0\left(\sqrt{x}+1>0\right)\\ \Leftrightarrow x>1\)