Rút gọn biểu thức: P=left(frac1-a sqrta1-sqrta+sqrtaright)

Với $a \geq 0 a \neq 1$ ta có: $a=(\sqrt{a})^{2}=\sqrt{a^{2}}$

$P=\left(\frac{1-a \sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right) \cdot\left(\frac{1-\sqrt{a}}{1-a}\right)^{2}$

$=\left(\frac{(1-\sqrt{a})\left(1+\sqrt{a}+\sqrt{a^{2}}\right)}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1-\sqrt{a}}{(1-\sqrt{a})(1+\sqrt{a})}\right)^{2}$

$=(1+\sqrt{a}+a+\sqrt{a}) \cdot\left(\frac{1}{1+\sqrt{a}}\right)^{2}=(1+2 \sqrt{a}+a) \cdot \frac{1}{(1+\sqrt{a})^{2}}$

$=(1+\sqrt{a})^{2} \cdot \frac{1}{(1+\sqrt{a})^{2}}=1$