What is the excluded value? y2-y+5/y+4

The given term is:  

Since here, the numerator i.e.  cannot be factorized. 

SO, the only excluded value is found on the basis of the denominator. The denominator should not be equal to 0, otherwise, the fraction will turn out to be zero.
SO, if y  -4, then denominator will not be zero.
Therefore, the excluded value is -4

The excluded value is the number that would make the denominator equal to zero. For a function, the excluded value is the number, or numbers, that are not in the domain of the function.

In this case, the excluded value is -4, since, if we plug in -4 for y, the denominator will be equal to zero and therefore the fraction will not be a real number. 

Answer is -4

a hypothesis is a educated guess