Question

Rút gọn \(\left(\frac{1-x\sqrt{x}}{1-\sqrt{x}}\right)\left(\frac{1-\sqrt{x}}{1-x}\right)^2\)

Answer 1

\(\text{ĐKXĐ: }x\ge0;x\ne1\)

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

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

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