an object has a mass of m= 3x/4x^2 and density of d=x-1/2^2 where ve m/d and state any restrictions on the variable.

So this simplifies to v=3x/2x-2 my question is the restriction i have found is x cannot be 1 which would make the denominator zero. Do I have to be concerned with the numerator as well. Should another restriction also be x cannot equal zero because that would make the numerator zero?

numerator zero is no problem.

0/x = 0 for any nonzero x.

The only restrictions you need worry about are where the denominator is zero.