Given: \(\frac{1}{y} − \frac{1}{(y+1)} = \frac{1}{(y+4)}\)

To eliminate the fractions, we'll multiply both sides of the equation by the least common multiple of y, y+1, and y+4

So, multiply both sides by (y)(y+1)(y+4) to get: (y+1)(y+4) - (y)(y+4) = (y)(y+1)
Expand to get: [y² + 5y + 4] - [y² + 4y] = y² + y
Simplify: y + 4 = y² + y
Subtract y from both sides to get: 4 = y²
So, y = 2 or y = -2

The SUM of the solutions = 2 + (-2) = 0

Answer: C

Cheers,
Brent