Question

P= ( \(\sqrt{x}-\dfrac{x+2}{\sqrt{x}+1}\)) : ( \(\dfrac{\sqrt{x}}{\sqrt{x}+1}-\dfrac{\sqrt{x}-4}{1-x}\)) +1

a) Rút gọn P

b) Tìm x để P = \(\dfrac{5}{7}\)

c) Tìm x để biểu thức P có giá trị nhỏ nhất

Answer 1

a: \(P=\dfrac{x+\sqrt{x}-x-2}{\sqrt{x}+1}:\dfrac{x-\sqrt{x}+\sqrt{x}-4}{x-1}+1\)

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

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

b: \(P=\dfrac{5}{7}\) nên \(5\left(\sqrt{x}+2\right)=7\left(2\sqrt{x}+1\right)\)

\(\Leftrightarrow14\sqrt{x}+7-5\sqrt{x}-10=0\)

\(\Leftrightarrow9\sqrt{x}=3\)

hay x=1/3