We can simplify the expression $\frac{1}{a - b} + \frac{1}{b - a}$ as follows:

Step 1: Notice the relationship between $a - b$ and $b - a$

We observe that $b - a = -(a - b)$. So, we can rewrite the second fraction using this relationship: $\frac{1}{a - b} + \frac{1}{-(a - b)}$

Step 2: Simplify the expression

Now we have: $\frac{1}{a - b} - \frac{1}{a - b}$

Step 3: Combine the terms

These two terms cancel each other out: $\frac{1}{a - b} - \frac{1}{a - b} = 0$

Thus, the simplified expression is: $0$

Do you have any questions or need further details?

Here are 5 related questions to expand your understanding:

1. What happens if $a = b$ in this expression?
2. How can you simplify other expressions with denominators that involve a negative sign?
3. What is the result of combining rational expressions with common denominators?
4. How can you factor common terms in a rational expression?
5. How can you simplify $\frac{1}{a+b} + \frac{1}{b+a}$?

Tip: Always look for common factors or relationships between terms when simplifying algebraic fractions.