Question

6.cho biểu thức : p =\(\left(\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1+\dfrac{\sqrt{x}}{x+1}\right)\)

a)rút gọn p

b)tìn x để p\(\le0\)

Answer 1

a: \(P=\left(\dfrac{2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}-1\right)}-\dfrac{1}{\sqrt{x}-1}\right):\dfrac{x+\sqrt{x}+1}{x+1}\)

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

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

b: Để P<=0 thì \(\dfrac{-\left(\sqrt{x}-1\right)}{x+\sqrt{x}+1}< =0\)

\(\Leftrightarrow\sqrt{x}-1>=0\)

hay x>1