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The image shows a math problem involving fractions, particularly simplifying or calculating the difference between two algebraic fractions.

The equation appears to be:

\[
\frac{a}{a - b} - \frac{b}{a + b}
\]

It seems like you're required to simplify this expression or perhaps find a common denominator to combine the fractions.

### To solve this:

1. **Find a common denominator**:
   - The denominators are \((a - b)\) and \((a + b)\).
   - The common denominator would be the product of the two, i.e., \((a - b)(a + b)\).

2. **Rewrite each fraction with the common denominator**:
   - The first fraction becomes:
     \[
     \frac{a}{a - b} \cdot \frac{a + b}{a + b} = \frac{a(a + b)}{(a - b)(a + b)}
     \]
   - The second fraction becomes:
     \[
     \frac{b}{a + b} \cdot \frac{a - b}{a - b} = \frac{b(a - b)}{(a - b)(a + b)}
     \]

3. **Combine the fractions**:
   \[
   \frac{a(a + b)}{(a - b)(a + b)} - \frac{b(a - b)}{(a - b)(a + b)}
   \]
   Now, both fractions have the same denominator, so they can be combined:
   \[
   \frac{a(a + b) - b(a - b)}{(a - b)(a + b)}
   \]

4. **Simplify the numerator**:
   Expand both terms in the numerator:
   \[
   a(a + b) = a^2 + ab
   \]
   \[
   b(a - b) = ab - b^2
   \]
   So the numerator becomes:
   \[
   (a^2 + ab) - (ab - b^2) = a^2 + ab - ab + b^2 = a^2 + b^2
   \]

5. **Final simplified form**:
   \[
   \frac{a^2 + b^2}{(a - b)(a + b)}
   \]

This is the simplified form of the given expression.

Would you like further details or have any questions about this? 

### Related Questions:
1. What are the steps to multiply two binomials like \((a - b)\) and \((a + b)\)?
2. How can we expand the expression \(a(a + b)\) and \(b(a - b)\)?
3. Why is it important to find a common denominator when adding or subtracting fractions?
4. What are some common mistakes to avoid when simplifying algebraic fractions?
5. How can this method be applied to fractions with different kinds of denominators?

### Tip:
Always double-check each step for signs and operations when simplifying algebraic fractions to avoid errors!

Simplify the expression: (a / (a - b)) - (b / (a + b))

Learn how to simplify the algebraic expression (a / (a - b)) - (b / (a + b)) by finding a common denominator and combining fractions. This step-by-step guide covers core algebraic concepts such as fraction subtraction, common denominators, and simplification techniques. Suitable for students in Grades 8-10.

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