To solve the given expression, we need to perform the division and addition operations in the correct order. First, divide 21 by 4 and 21 by 3 separately, then add the results together.
Calculate \( \frac{21}{4} \).
\[ \frac{21}{4} = 5.25 \]
Calculate \( \frac{21}{3} \).
\[ \frac{21}{3} = 7 \]
Add the results from Step 1 and Step 2.
\[ 5.25 + 7 = 12.25 \]
The answer is \(\boxed{12.25}\).
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