Rút gọn các biểu thức sau
----- Nội dung ảnh -----
a) \( 10 + 2\sqrt{10} + 8 \)
\[
\frac{\sqrt{5} + \sqrt{2}}{1 - \sqrt{5}} = -2
\]
b) \( 2\sqrt{8 - \sqrt{12}} \)
\[
\frac{\sqrt{5} + 27}{\sqrt{18} - \sqrt{48}} = \frac{\sqrt{6}}{2}
\]
c) \( \frac{2 - \sqrt{3}}{2\sqrt{3}} + \frac{2 + \sqrt{3}}{2 - \sqrt{3}} = 4 \)
d) \( \frac{(3 - \sqrt{5})(3 + \sqrt{5})}{\sqrt{10} + \sqrt{2}} = 1 \)
e) \( 1 + \frac{1}{\sqrt{2 + \sqrt{2 + \sqrt{3}}} + \sqrt{2 - \sqrt{2 - \sqrt{3}}} \)
f) \( \frac{(\sqrt{5} + 2)^2 - 8\sqrt{5}}{2\sqrt{5} - 9} \)
a) \( 10 + 2\sqrt{10} + 8 \)
\[
\frac{\sqrt{5} + \sqrt{2}}{1 - \sqrt{5}} = -2
\]
b) \( 2\sqrt{8 - \sqrt{12}} \)
\[
\frac{\sqrt{5} + 27}{\sqrt{18} - \sqrt{48}} = \frac{\sqrt{6}}{2}
\]
c) \( \frac{2 - \sqrt{3}}{2\sqrt{3}} + \frac{2 + \sqrt{3}}{2 - \sqrt{3}} = 4 \)
d) \( \frac{(3 - \sqrt{5})(3 + \sqrt{5})}{\sqrt{10} + \sqrt{2}} = 1 \)
e) \( 1 + \frac{1}{\sqrt{2 + \sqrt{2 + \sqrt{3}}} + \sqrt{2 - \sqrt{2 - \sqrt{3}}} \)
f) \( \frac{(\sqrt{5} + 2)^2 - 8\sqrt{5}}{2\sqrt{5} - 9} \)