Question 43122
The best way is to first get rid of the fractions.  That is what makes these problems so confusing:

Get rid of the fractions by multiplying by a common factor:
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Multiply the entire equation by 6 which is common to both 3 and 6.
6(x/3 - x/6 = 1)
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Distribute the 6 throughout the equation:

6x/3 - 6x/6 = (6)(1)
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Cancel out wherever possible:
2x-x=6
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Simplify by combining like-terms:
x =6

Check your answer by plugging x=6 back into the original equation:
x/3 - x/6 = 1
(6)/3 - (6)/6 = 1
2-1=1
1=1  It checks out.