a.
\(A=\frac{1}{2\sqrt{3}-2}-\frac{1}{2\sqrt{3}+2}\\ =\frac{2\sqrt{3}+2-2\sqrt{3}+2}{\left(2\sqrt{3}+2\right)\left(2\sqrt{3}-2\right)}\\ =\frac{4}{\left(2\sqrt{3}\right)^2-2^2}=\frac{4}{8}=\frac{1}{2}\)
\(B=\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}-1}{x-\sqrt{x}}\left(ĐK:x>0;x\ne1\right)\\ =\frac{\left(\sqrt{x}\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{2\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)}\\ =\frac{x-2\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}\\ =\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}-1}{\sqrt{x}}\)
b.
\(B=\frac{2}{5}A\Leftrightarrow\frac{\sqrt{x}-1}{\sqrt{x}}=\frac{2}{5}\cdot\frac{1}{2}=\frac{1}{5}\\ \Leftrightarrow\frac{\sqrt{x}-1}{\sqrt{x}}-\frac{1}{5}=0\\ \Leftrightarrow\frac{5\left(\sqrt{x}-1\right)-\sqrt{x}}{5\sqrt{x}}=0\\ \Leftrightarrow\frac{4\sqrt{x}-5}{5\sqrt{x}}=0\\ \Rightarrow4\sqrt{x}-5=0\\ \Leftrightarrow\sqrt{x}=\frac{5}{4}\Rightarrow x=\frac{25}{16}\)
(Bạn kiểm tra xem kết quả số có đúng ko nha)
