To simplify the expression \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \), we can start by combining like terms.
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Combine the \( x \) terms: \[ \frac{3}{10}x + \frac{3}{10}x = \left(\frac{3}{10} + \frac{3}{10}\right)x = \frac{6}{10}x \] Simplifying \( \frac{6}{10} \) gives: \[ \frac{6}{10} = \frac{3}{5} \] So we have \( \frac{3}{5}x \).
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Combine the \( y \) terms: \[ \frac{1}{6}y + \frac{3}{6}y = \left(\frac{1}{6} + \frac{3}{6}\right)y = \frac{4}{6}y \] Simplifying \( \frac{4}{6} \) gives: \[ \frac{4}{6} = \frac{2}{3} \] So we have \( \frac{2}{3}y \).
Now, putting it all together, the expression becomes: \[ \frac{3}{5}x + \frac{2}{3}y \]
Thus, the simplified expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]