Only the first one here is a fraction, so perhaps you copied the second one incorrectly. Nonetheless, we can certainly solve the fraction.
As fractions are considered "undefined" if the denominator equals zero, the only way for a fraction to equal zero is for the numerator to equal zero - no matter the value of the denominator. In the case of x(x+1)/x+4, either x=0 or x+1=0. So:
0(0+1)/0+4 = 0/4
-1(0)/-1+4 = 0/3
So, x=-1 & x=0 will make the fraction equal zero.