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\frac{3\left(x+y\right)}{3}+\frac{z}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply x+y times \frac{3}{3}.
\frac{3\left(x+y\right)+z}{3}
Since \frac{3\left(x+y\right)}{3} and \frac{z}{3} have the same denominator, add them by adding their numerators.
\frac{3x+3y+z}{3}
Do the multiplications in 3\left(x+y\right)+z.
\frac{3x+3y+z}{3}
Factor out \frac{1}{3}.