The expression you've provided is:

$\frac{x}{x+1} + \frac{1}{x+1}$

Since both fractions have the same denominator $(x+1)$, you can combine them into a single fraction:

$\frac{x + 1}{x+1}$

Now, since the numerator and denominator are the same, this simplifies to:

$1$

So, the simplified expression is:

$\frac{x}{x+1} + \frac{1}{x+1} = 1$

Would you like more details on this, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How would you simplify $\frac{2x}{x+2} + \frac{2}{x+2}$?
2. What happens if you simplify $\frac{x+1}{x} + \frac{1}{x}$?
3. Can you find the derivative of $\frac{x}{x+1}$?
4. How do you solve the equation $\frac{x}{x+1} + \frac{1}{x+1} = 2$?
5. What is the value of $\frac{x}{x+1} + \frac{1}{x+1}$ when $x = 3$?

Tip: When combining fractions, always check if they have the same denominator. If they do, you can directly add or subtract the numerators.