Question

Rút gọn

\(\left(\dfrac{3+\sqrt{X}}{X+\sqrt{X}+1}-\dfrac{\sqrt{X}-3}{X\sqrt{X}-1}\right):\dfrac{X^2+X\sqrt{X}-\sqrt{X}-1}{\sqrt{X}}\)

Answer 1

\(=\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}-3\right)}{x\sqrt{x}-1}\cdot\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x\sqrt{x}-1\right)}\)

\(=\dfrac{x+2\sqrt{x}-3-\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)^2\cdot\left(x+\sqrt{x}+1\right)}\)

\(=\dfrac{x\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)^3\cdot\left(x+\sqrt{x}+1\right)^2}\)