Question: User: b=12/b+1
1. **State the problem:** Solve the equation $b = \frac{12}{b} + 1$ for $b$.
2. **Rewrite the equation:**
$$b = \frac{12}{b} + 1$$
3. **Multiply both sides by $b$ to eliminate the denominator:**
$$b \times b = b \times \left(\frac{12}{b} + 1\right)$$
$$b^2 = 12 + b$$
4. **Bring all terms to one side to form a quadratic equation:**
$$b^2 - b - 12 = 0$$
5. **Factor the quadratic equation:**
$$b^2 - b - 12 = (b - 4)(b + 3) = 0$$
6. **Set each factor equal to zero and solve for $b$:**
$$b - 4 = 0 \Rightarrow b = 4$$
$$b + 3 = 0 \Rightarrow b = -3$$
7. **Check for extraneous solutions by substituting back into the original equation:**
- For $b=4$:
$$4 = \frac{12}{4} + 1 = 3 + 1 = 4$$ (valid)
- For $b=-3$:
$$-3 = \frac{12}{-3} + 1 = -4 + 1 = -3$$ (valid)
**Final answer:** $b = 4$ or $b = -3$