Rút gọn biểu thức

- Hướng dẫn giải

Ta có: $\frac{4a}{\sqrt{7}-\sqrt{3}}-\frac{2a}{2-\sqrt{2}}-\frac{a}{\sqrt{3}+\sqrt{2}}$

$=\frac{4a\left(\sqrt{7}+\sqrt{3}\right)}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}-\frac{2a\left(2+\sqrt{2}\right)}{\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)}-\frac{a\left(\sqrt{3}-\sqrt{2}\right)}{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}$

$$\begin{gathered} =a\left(\sqrt{7}+\sqrt{3}\right)-a\left(2+\sqrt{2}\right)-a\left(\sqrt{3}-\sqrt{2}\right) \\ =a\left(\sqrt{7}+\sqrt{3}-2-\sqrt{2}-\sqrt{3}+\sqrt{2}\right) \end{gathered}$$

$=a\left(\sqrt{7}-2\right)$

Đáp án cần chọn là: D