Simplify each complex fraction. [ (y+3)/y - 4/(y-1) ] / [ y/(y - 1) + 1/y ]

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1. Identify the complex fraction: \( \frac{\frac{y+3}{y} - \frac{4}{y-1}}{\frac{y}{y-1} + \frac{1}{y}} \).
2. Find a common denominator for the fractions in the numerator: The common denominator for \( \frac{y+3}{y} \) and \( \frac{4}{y-1} \) is \( y(y-1) \).
3. Rewrite the numerator: \( \frac{(y+3)(y-1) - 4y}{y(y-1)} \).
4. Find a common denominator for the fractions in the denominator: The common denominator for \( \frac{y}{y-1} \) and \( \frac{1}{y} \) is \( y(y-1) \).
5. Rewrite the denominator: \( \frac{y^2 + (y-1)}{y(y-1)} \).