jmc

Combining the fractions on the left gives $\frac{n+3}{n+1}=3$. Multiplying both sides by $n+1$ gives $n+3=3(n+1)$. Expanding the right side gives $n+3=3n+3$. Subtracting $n$ and 3 from both sides gives $0=2n$, so $n=\boxed{0}$.