Question

Cho biểu thức: A=\(\left(\frac{3+\sqrt{x}}{x+2\sqrt{x}+1}-\frac{\sqrt{x}-3}{x-1}\right).\frac{x\sqrt{x}+x-\sqrt{x}-1}{x\sqrt{x}}\)

Answer 1

đkxđ x>0;x≠1

(\(\frac{3+\sqrt{x}}{\left(\sqrt{x}+1\right)^2}\)-\(\frac{\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)).\(\frac{\left(\sqrt{x}+1\right)^2\left(\sqrt{x}-1\right)}{x\sqrt{x}}\)=\(\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}{x\sqrt{x}}\)=\(\frac{x+2\sqrt{x}-3-x+2\sqrt{x}+3}{x\sqrt{x}}\)=\(\frac{4\sqrt{x}}{x\sqrt{x}}\)=\(\frac{4}{x}\)