We can simplify the given expression:

$\frac{(y+1)}{(y+1)^2} + \frac{3}{y+1}$

Step 1: Simplify the first term

The first term simplifies as follows: $\frac{(y+1)}{(y+1)^2} = \frac{1}{y+1}$

So now the expression becomes: $\frac{1}{y+1} + \frac{3}{y+1}$

Step 2: Combine like terms

Both terms have the same denominator $(y+1)$, so we can combine them: $\frac{1 + 3}{y+1} = \frac{4}{y+1}$

Final Answer:

$\frac{4}{y+1}$

Would you like any more details or have any further questions?

Here are 5 related questions to explore:

1. How can I simplify rational expressions with different denominators?
2. How do you factor polynomials with common terms?
3. What is the process for finding common denominators in algebraic fractions?
4. How do you simplify expressions with exponents?
5. How do you solve rational equations involving variables in the denominator?

Tip: Always look for common denominators when combining fractions to simplify algebraic expressions faster!