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Question
What should be added to \[\left( \frac{1}{2} + \frac{1}{3} + \frac{1}{5} \right)\] to get 3?
Sum
Solution
\[\text{Let x be added .} \]
\[ \therefore x + (\frac{1}{2} + \frac{1}{3} + \frac{1}{5}) = 3\]
\[ \Rightarrow x + (\frac{15}{30} + \frac{10}{30} + \frac{6}{30}) = 3\]
\[ \Rightarrow x + (\frac{15 + 10 + 6}{30}) = 3\]
\[ \Rightarrow x + \frac{31}{30} = 3\]
\[ \Rightarrow x = \frac{3}{1} - \frac{31}{30}\]
\[ \Rightarrow x = \frac{90}{30} - \frac{31}{30}\]
\[ \Rightarrow x = \frac{90 - 31}{30}\]
\[ \Rightarrow x = \frac{59}{30}\]
\[ \therefore x + (\frac{1}{2} + \frac{1}{3} + \frac{1}{5}) = 3\]
\[ \Rightarrow x + (\frac{15}{30} + \frac{10}{30} + \frac{6}{30}) = 3\]
\[ \Rightarrow x + (\frac{15 + 10 + 6}{30}) = 3\]
\[ \Rightarrow x + \frac{31}{30} = 3\]
\[ \Rightarrow x = \frac{3}{1} - \frac{31}{30}\]
\[ \Rightarrow x = \frac{90}{30} - \frac{31}{30}\]
\[ \Rightarrow x = \frac{90 - 31}{30}\]
\[ \Rightarrow x = \frac{59}{30}\]
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