Final answer:
To simplify the given rational expression, factor the second denominator, find a common denominator, combine the fractions, and simplify the numerator to end with (x - 1)/(x-4).
Step-by-step explanation:
To simplify the rational expression (x+2)/(x-4) - 1/(3x-12), we first look for common factors in the denominators. Notice that 3x-12 can be factored as 3(x-4), which reveals that both denominators have (x-4) in common.
Now, to create a common denominator, we multiply the numerator and the denominator of the second fraction by 3, giving us:
(x+2)/(x-4) - 3/(3(x-4))
With a common denominator of (x-4), we can combine the fractions:
((x+2) - 3)/(x-4)
Simplifying the numerator, we get:
(x - 1)/(x-4)
This is the simplified form of the given rational expression.