| The value of \[\frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}\]will be |
A) \[\frac{39}{109}\]
B) \[\frac{109}{38}\]
C) \[\frac{38}{109}\]
D) \[\frac{116}{109}\]
Correct Answer: C
Solution :
| \[\frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}=\frac{\frac{7}{3}-\frac{13}{11}}{3+\frac{1}{3+\frac{1}{\frac{9+1}{3}}}}\] |
| \[=\frac{\frac{77-39}{33}}{3+\frac{1}{3+\frac{3}{10}}}=\frac{38/33}{3+\frac{1}{\frac{30+3}{10}}}=\frac{38/33}{3+\frac{10}{33}}\] |
| \[=\frac{38/33}{\frac{99+10}{33}}=\frac{38/33}{109/33}=\frac{38}{109}\] |
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