a) $$ \frac{x-3}{3}-\frac{x-2}{2}+\frac{x+1}{6} $$

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Calculate or simplify the expression $$ (x-3)/3-(x-2)/2+(x+1)/6 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(x-3ight)}{3}-\frac{\left(x-2ight)}{2}+\frac{\left(x+1ight)}{6}$$
- step1: Remove the parentheses:
  $$\frac{x-3}{3}-\frac{x-2}{2}+\frac{x+1}{6}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{\left(x-3ight)	imes 2}{3	imes 2}-\frac{\left(x-2ight)	imes 3}{2	imes 3}+\frac{x+1}{6}$$
- step3: Multiply the numbers:
  $$\frac{\left(x-3ight)	imes 2}{6}-\frac{\left(x-2ight)	imes 3}{2	imes 3}+\frac{x+1}{6}$$
- step4: Multiply the numbers:
  $$\frac{\left(x-3ight)	imes 2}{6}-\frac{\left(x-2ight)	imes 3}{6}+\frac{x+1}{6}$$
- step5: Transform the expression:
  $$\frac{\left(x-3ight)	imes 2-\left(x-2ight)	imes 3+x+1}{6}$$
- step6: Multiply the terms:
  $$\frac{2x-6-\left(x-2ight)	imes 3+x+1}{6}$$
- step7: Multiply the terms:
  $$\frac{2x-6-\left(3x-6ight)+x+1}{6}$$
- step8: Calculate:
  $$\frac{1}{6}$$
The simplified form of the expression $$ \frac{x-3}{3}-\frac{x-2}{2}+\frac{x+1}{6} $$ is $$ \frac{1}{6} $$ or $$ 0.1\dot{6} $$.
The simplified form of the expression is $$ \frac{1}{6} $$ or $$ 0.1\dot{6} $$.

a) \( \frac{x-3}{3}-\frac{x-2}{2}+\frac{x+1}{6} \)

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