To simplify the expression \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \), we first combine like terms.
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Combine the \( x \) terms: \[ \frac{3}{10}x + \frac{3}{10}x = \frac{6}{10}x = \frac{3}{5}x \]
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Combine the \( y \) terms: \[ \frac{1}{6}y + \frac{3}{6}y = \frac{4}{6}y = \frac{2}{3}y \]
Now, we can rewrite the entire expression: \[ \frac{3}{5}x + \frac{2}{3}y \]
There are no further simplifications, and the expression in its simplest form is: \[ \frac{3}{5}x + \frac{2}{3}y \]
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