$\displaystyle \frac{3-\sqrt{5}(2cos\theta )}{3-\sqrt{5}(cos\theta )}$
The answer to your question is purely subjective.
My answer is NO!.
Before the age of calculators or computer algebra systems we wanted students to "rationalize".
It made approximations easier and more actuate.
But that is no longer an issue.
But you must defer to your instructor on this matter.
It is an issue of whether you want your fraction to make sense. All surds can be written as finite lengths, and it makes sense to divide a finite length into a countable number of pieces. It does not however make sense to divide any length into an uncountable number of pieces.
generally speaking we avoid irrational numbers in the denominator. We get rid of these irrational by multiplying and dividing be the rationalizing factor of the denominator, which in this case is ( 3 + Sqr root 5 cos theta)