What is the excluded value of y^2-y+5/y+4

excluded value is x = - 4

The denominator of the rational expression cannot be zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the value that y cannot be.

solve y + 4 = 0 ⇒ y = - 4 ← excluded value

if y+4 = 0 or y=-4 we have division by 0 and therefore

y=-4 is excluded