To simplify the expression:

\[
\frac{a + b}{a^2 - b^2} - \frac{a - b}{a^2 - b^2}
\]

### Step 1: Recognize a common denominator
The denominators in both fractions are the same: \( a^2 - b^2 \). We can factor this as a difference of squares:

\[
a^2 - b^2 = (a - b)(a + b)
\]

Thus, the expression becomes:

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

### Step 2: Combine the numerators
Since the denominators are the same, we can combine the two fractions:

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

### Step 3: Simplify the numerator
Simplify the numerator by distributing the negative sign in the second term:

\[
(a + b) - (a - b) = a + b - a + b = 2b
\]

### Step 4: Final simplified expression
Now substitute the simplified numerator:

\[
\frac{2b}{(a - b)(a + b)}
\]

Thus, the simplified expression is:

\[
\frac{2b}{(a - b)(a + b)}
\]

Would you like further details or any clarifications?

Here are five related questions:
1. How do you factor more complex quadratic expressions?
2. What is the difference of squares identity used for?
3. Can this expression be simplified further if \( b = 0 \)?
4. What happens when \( a = b \)?
5. How do you solve an equation involving fractions with polynomial denominators?

**Tip:** Always check for common factors in numerators and denominators to simplify fractions.

Simplify a + b / a^2 - b^2 - a - b / a^2 - b^2

This problem simplifies a rational expression using the difference of squares. Learn how to simplify the expression a + b / a^2 - b^2 - a - b / a^2 - b^2 step-by-step, covering key algebraic concepts such as factoring and combining like terms. Suitable for students in Grades 9-11.

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