To simplify the expression \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \), we can follow these steps:
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Combine like terms:
- For the \(x\) terms: \( \frac{3}{10}x + \frac{3}{10}x = \frac{6}{10}x \)
- For the \(y\) terms: \( \frac{1}{6}y + \frac{3}{6}y = \frac{4}{6}y \)
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Simplify the fractions:
- For the \(x\) term: \( \frac{6}{10}x \) can be simplified by dividing the numerator and denominator by 2: \[ \frac{6 \div 2}{10 \div 2}x = \frac{3}{5}x \]
- For the \(y\) term: \( \frac{4}{6}y \) can be simplified by dividing the numerator and denominator by 2: \[ \frac{4 \div 2}{6 \div 2}y = \frac{2}{3}y \]
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Combine the simplified terms:
- The final expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]
So, the simplified expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]