Question

[KHANH QUYNH MAI PHAM]

Tính biểu thức

(\(\frac{2x+1}{\sqrt{x^3}-1}-\)\(\frac{\sqrt{x}}{x+\sqrt{x}+1}\)):(\(\frac{1+\sqrt{x^3}}{1+\sqrt{x}}-\sqrt{x}\))

Answer 1

[Phạm Thị Thùy Linh]

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

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

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

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

\(=\frac{1}{\left(\sqrt{x}-1\right)^3}\)