A) 0
B) 1
C) 3
D) \[3+\sqrt{3}\]
Correct Answer: C
Solution :
| \[\frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}\] |
| \[\frac{1}{3+\sqrt{3}}=\frac{1}{3+\sqrt{3}}\times \frac{3-\sqrt{3}}{3-\sqrt{3}}=\frac{3-\sqrt{3}}{9-3}=\frac{3-\sqrt{3}}{6}\] |
| \[\frac{1}{\sqrt{3}-3}=\frac{1}{\sqrt{3}-3}\times \frac{\sqrt{3}+3}{\sqrt{3}+3}=\frac{\sqrt{3}+3}{-\,\,6}\] |
| Given expression \[=3+\frac{\sqrt{3}}{3}+\frac{3-\sqrt{3}}{6}-\frac{\sqrt{3}-3}{6}\] |
| \[=3+\frac{\sqrt{3}}{3}+\frac{1}{2}-\frac{\sqrt{3}}{6}-\frac{\sqrt{3}}{6}-\frac{1}{2}\] |
| \[=3+\frac{\sqrt{3}}{3}-\frac{2\sqrt{3}}{6}=3+\frac{\sqrt{3}}{3}-\frac{\sqrt{3}}{3}=3\] |
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