1. Stated problem: Solve the equation $2 - \frac{1}{\alpha+1} = 0$ for $\alpha$. 2. Move the fraction to the other side: $$2 = \frac{1}{\alpha+1}$$ 3. Take the reciprocal of both sides: $$\frac{1}{2} = \alpha + 1$$ 4. Subtract 1 from both sides to isolate $\alpha$: $$\alpha = \frac{1}{2} - 1$$ 5. Simplify the right side: $$\alpha = \frac{1}{2} - \frac{2}{2} = -\frac{1}{2}$$ Final answer: $$\alpha = -\frac{1}{2}$$