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.

Discover how to simplify the algebraic expression 1/(a - b) + 1/(b - a). This problem involves understanding rational expressions and the relationship between negative denominators. It provides a step-by-step explanation for students in Grades 8-10.

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