Find the value of $n$ that satisfies $\frac{1}{n+1} + \frac{2}{n+1} + \frac{n}{n+1} = 3$.
To solve for $n$, I need to isolate it on one side of the equation. I notice that all the fractions on the left have the same denominator, $n+1$, so I can combine them by adding their numerators. That gives me $\frac{3+n}{n+1} = 3$. To get rid of the fraction on the left, I can multiply both sides by $n+1$. That gives me $3+n = 3(n+1)$. Expanding the right side, I get $3+n = 3n+3$. Subtracting $n$ from both sides, I get $3 = 2n+3$. Subtracting $3$ from both sides, I get $0 = 2n$. Dividing both sides by $2$, I get $n = 0$. This is the value of $n$ that satisfies the equation.

