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\frac{2\times 3}{3}-\frac{z}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.
\frac{2\times 3-z}{3}
Since \frac{2\times 3}{3} and \frac{z}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{6-z}{3}
Do the multiplications in 2\times 3-z.
\frac{6-z}{3}
Factor out \frac{1}{3}.