The expression you've provided can be clarified as:

\[
(1 - 2) \cdot \left(a + \frac{a}{a - 1}\right)
\]

Let's solve it step by step.

### Step 1: Simplify the Expression Inside the Parentheses
1. The first part of the expression is \((1 - 2)\), which simplifies to:
   \[
   -1
   \]

2. Now, focus on the second part, \(a + \frac{a}{a - 1}\):
   \[
   a + \frac{a}{a - 1} = \frac{a(a - 1) + a}{a - 1}
   \]

3. Distribute \(a\) in the numerator:
   \[
   = \frac{a^2 - a + a}{a - 1}
   \]

4. Simplify the terms:
   \[
   = \frac{a^2}{a - 1}
   \]

### Step 2: Substitute and Multiply
Substitute back into the expression:
\[
-1 \cdot \frac{a^2}{a - 1} = -\frac{a^2}{a - 1}
\]

### Final Answer
\[
-\frac{a^2}{a - 1}
\]

Would you like a more detailed explanation, or do you have any questions?

---

1. What if \(a = 1\) in the expression?  
2. How does the final expression behave as \(a\) gets very large?
3. How do you simplify complex fractions?
4. What if we used different variables instead of \(a\)?
5. How does this expression change if we replace \(1 - 2\) with another number?

**Tip:** Simplifying each part separately can make complex expressions more manageable.

Explore how to simplify the expression (1 - 2) • (a + a / (a - 1)) with a step-by-step breakdown. This problem demonstrates key algebraic principles, including rational expressions and distributive property, suitable for students in Grades 9-10.

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