I presume you know that you cannot divide by 0 so where is $\displaystyle 4- x^2= 0$? Also, you cannot take the square root of a negative number. A fraction is positive if both numerator and denominator are positive or if both numerator and denominator are negative. So if x> 0 where is [itex]4- x^2[/itex] also positive? If x< 0 is where is [itex]4- x^2[/itex]?
domain would be (-infinity,-2)U[0,2)
easy prob find roots of numerator and denominator that come out to be 0,2,-2 now plot on number line with alternate signs with given intervals where positive thats ur domain part then union it