Final answer:
To simplify the expression (x-3)/(6x)-(x+3)/(6x), find a common denominator, expand the expressions, combine like terms, and subtract the fractions.
Step-by-step explanation:
To simplify the expression (x-3)/(6x)-(x+3)/(6x), we need to find a common denominator for the two fractions. The common denominator is 6x. We then multiply the numerators by the appropriate terms to get:
(x-3)(x)/(6x) - (x+3)(-3)/(6x)
Expanding the expressions and combining like terms, we have:
(x²-3x)/(6x) - (-3x-9)/(6x)
Now, we can subtract the two fractions:
((x²-3x) - (-3x-9))/(6x)
Combining like terms again, we get:
(x²-3x+3x+9)/(6x)
Simplifying further, we have:
(x²+6)/(6x)