What do you mean "eliminate negative exponents?" There's nothing wrong with writing x^-1 instead of 1/x. Sometimes it's better left that way.
For example, it's a lot easier to multiply x^2 + x^-1 times x^-2 + x^3 than to multiply (x^3 + 1)/x times (x^5 + 1)/x^2.
On the other hand, if you want to set a rational function equal to zero, it helps to get it in a quotient form with only positive exponents, since you can then go ahead and (almost) ignore the denominator. (Of course at the end you have to check that your solutions don't make the denominator equal to zero).
So it really depends on the situation.
==================================== Judy Roitman, Mathematics Department Univ. of Kansas, Lawrence, KS 66049 email@example.com =====================================