To simplify the expression \(\frac{29}{4} + \frac{34}{7} + \frac{39}{4}\), we can first combine the fractions with the same denominator and then add them all together.
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Combine the fractions with a common denominator. The fractions \(\frac{29}{4}\) and \(\frac{39}{4}\) have the same denominator, so we can add them directly: \[ \frac{29}{4} + \frac{39}{4} = \frac{29 + 39}{4} = \frac{68}{4} \]
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Now simplify \(\frac{68}{4}\): \[ \frac{68}{4} = 17 \]
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Now we need to add \(\frac{34}{7}\) to the result: \[ 17 + \frac{34}{7} \]
To add these together, we convert 17 to a fraction with a denominator of 7: \[ 17 = \frac{17 \times 7}{7} = \frac{119}{7} \]
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Now add \(\frac{119}{7} + \frac{34}{7}\): \[ \frac{119 + 34}{7} = \frac{153}{7} \]
Thus, the simplified expression is: \[ \frac{153}{7} \]
If desired, \(\frac{153}{7}\) can also be expressed as a mixed number: \[ \frac{153}{7} = 21 \frac{6}{7} \]
So, the final simplified expression can be written as either \(\frac{153}{7}\) or \(21 \frac{6}{7}\).