Question

\(\left(\frac{x}{\sqrt{x}-1}-\sqrt{x}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}}-\frac{1}{1-\sqrt{x}}+\frac{2-x}{x-\sqrt{x}}\right)\)

a. rút gọn m

b. tính gt của M khi x = 7 + 4\(\sqrt{3}\)

c. tìm x sao cho M = 1/2

Answer 1

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

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

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

=\(\frac{\sqrt{x}}{\sqrt{x}+1}\)

Answer 2

b) Thay x= \(7+4\sqrt{3}\) ta được

\(\frac{\sqrt{7+4\sqrt{3}}}{\sqrt{7+4\sqrt{3}}+1}=\frac{2-\sqrt{3}}{3-\sqrt{3}}\)

Answer 3

c) \(\frac{\sqrt{x}}{\sqrt{x}+1}=\frac{1}{2}\Leftrightarrow2\sqrt{x}=\sqrt{x}+1\)

\(\Leftrightarrow\sqrt{x}=1\Leftrightarrow x=1\)