(18n2-9n+1)/(3n-1) is not a problem that you can SOLVE; solving is reserved for an equation (you find values of the variable that make the equation true).
What you have is a "rational algebraic expression"--such things may be simplified. The essence of this is to factor the numerator. Before cancelling any of its factors by an identical factor in the denominator, you ought to note the Domain restriction(s); in this case, n must not be 1/3.
Your simplification will lead you to declare that the original expression is equivalent to 6n-1. This is true but the restriction n ≠1/3 still must be kept.