Since many people do not like to have any sort of radical in a denominator, we can get rid of this by multiplying the numerator and denominator by 1-√3....so we have
-4 / (1+√3) * (1-√3) / (1-√3)
The denominator of the resulting fraction becomes (1 -3) = -2
So we have ... (-4)*(1-√3) /( -2) = 2 (1-√3)
Note how this procedure leaves us with no fraction at all......however, we still have a "nasty" radical hanging around....!!!