https://file.aiquickdraw.com/mathbot/file/1727368907243qfjj4qpu.jpg

The question in the image asks for the simplified form of the expression:

\[
\frac{5 - c}{c^2 - c - 20}
\]

### Step-by-step solution:

1. **Factor the denominator**: We need to factor \( c^2 - c - 20 \). This is a quadratic expression, and we factor it by finding two numbers that multiply to \(-20\) and add to \(-1\).

   Factors of \(-20\) are \((4, -5)\), since:
   \[
   4 \times (-5) = -20 \quad \text{and} \quad 4 + (-5) = -1
   \]

   Thus, we can factor the denominator as:
   \[
   c^2 - c - 20 = (c - 5)(c + 4)
   \]

2. **Rewrite the expression**: The given expression becomes:
   \[
   \frac{5 - c}{(c - 5)(c + 4)}
   \]

3. **Simplify the expression**: Notice that \( 5 - c \) is the negative of \( c - 5 \). Specifically:
   \[
   5 - c = -(c - 5)
   \]
   So we can rewrite the expression as:
   \[
   \frac{-(c - 5)}{(c - 5)(c + 4)}
   \]

4. **Cancel common factors**: The \( (c - 5) \) terms cancel out, leaving us with:
   \[
   \frac{-1}{c + 4}
   \]

Thus, the simplified form is:

\[
\frac{-1}{c + 4}
\]

### Correct Answer:
The correct choice from the options in the image is **D**.

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Do you want more details on any part of the solution? Here are 5 related questions:

1. How do you factor quadratic expressions like \( c^2 - c - 20 \)?
2. Why does \( 5 - c = -(c - 5) \) when simplifying expressions?
3. Can you explain how to cancel terms in fractions properly?
4. What are other methods to simplify rational expressions?
5. What happens when a quadratic expression has no real factors?

**Tip:** Always look for factoring opportunities when simplifying complex rational expressions!

What is the simplified form of the expression (5 - c) / (c^2 - c - 20)?

Learn how to simplify the rational expression (5 - c) / (c^2 - c - 20) by factoring the quadratic denominator and canceling common terms. This problem demonstrates key algebraic techniques suitable for students in Grades 8-10.

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