https://file.aiquickdraw.com/mathbot/file/1729070890436ezlzg7t5.jpg

The problem in the image involves simplifying a mathematical expression. The given expression is:

\[
\frac{1 - \frac{a}{1}}{1 + \frac{a}{1-a}}
\]

### Let's simplify this step by step:

1. **Simplify the numerator:**
   \[
   1 - \frac{a}{1} = 1 - a
   \]
   So, the numerator becomes \( 1 - a \).

2. **Simplify the denominator:**
   \[
   1 + \frac{a}{1 - a}
   \]
   We leave this as is for now.

So, the overall expression becomes:

\[
\frac{1 - a}{1 + \frac{a}{1 - a}}
\]

3. **Simplify the denominator further:**
   To simplify this, combine the terms in the denominator:
   \[
   \frac{1 - a}{1 + \frac{a}{1 - a}} = \frac{1 - a}{\frac{(1 - a) + a}{1 - a}}
   \]

   Simplifying the term inside the denominator:
   \[
   (1 - a) + a = 1
   \]

   So the denominator becomes:
   \[
   \frac{1}{1 - a}
   \]

4. **Final simplification:**
   The expression now becomes:
   \[
   \frac{1 - a}{\frac{1}{1 - a}} = (1 - a) \times (1 - a) = (1 - a)^2
   \]

### Conclusion:
The simplified expression is \( (1 - a)^2 \).

Looking at the answer choices, the correct one appears to be **C: 1 - a**. However, based on our calculations, it should be \( (1 - a)^2 \), which might be a slight mismatch in the choices provided.

Do you want to go into more detail about any step or discuss further questions? Here are five related questions you might find helpful:

1. What are common errors to watch out for when simplifying rational expressions?
2. How can you apply similar techniques to simplify more complex algebraic expressions?
3. How do you handle expressions with more complex fractions or nested fractions?
4. Could there be alternative approaches to simplifying this expression?
5. What conditions could make this expression undefined?

**Tip**: Always remember to simplify both the numerator and denominator separately before combining them for the final expression.

Simplify the expression (1 - a) / (1 + (a / (1 - a))) and find the correct answer.

Learn how to simplify the rational expression (1 - a) / (1 + (a / (1 - a))). This problem demonstrates key algebraic techniques for combining fractions and simplifying complex rational expressions. Suitable for students in Grades 9-12.

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