Question

cho biểu thức A=\(\left(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}\right).\frac{x-\sqrt{x}}{2\sqrt{x}+1}\)

rút gọn A

Answer 1

\(A=\left(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}\right).\frac{x-\sqrt{x}}{2\sqrt{x}+1}=\left(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{\left(\sqrt{x}\right)^2-1^2}\right).\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}+1}=\left(\frac{\sqrt{x}+1+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}+1}=\left(\frac{2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}+1}=\sqrt{x}\)