Let's evaluate the expression \( \frac{x^2 + x - 20}{x + 5} \) at \( x = -2 \).

### Step-by-step solution:
1. **Substitute** \( x = -2 \) into the expression:

\[
\frac{(-2)^2 + (-2) - 20}{-2 + 5}
\]

2. **Calculate the numerator**:

\[
(-2)^2 = 4
\]
\[
4 + (-2) - 20 = 4 - 2 - 20 = -18
\]

3. **Calculate the denominator**:

\[
-2 + 5 = 3
\]

4. **Now divide** the numerator by the denominator:

\[
\frac{-18}{3} = -6
\]

Thus, the value of the expression when \( x = -2 \) is \( \boxed{-6} \).

Would you like any further details or have any questions?

Here are five related questions to expand on this:
1. How do you simplify algebraic expressions involving fractions?
2. What happens if you substitute other values of \( x \) into the same expression?
3. How do you factor quadratic expressions like \( x^2 + x - 20 \)?
4. What are the steps to solve rational equations?
5. How do you handle expressions when the denominator becomes zero?

**Tip:** Always simplify both the numerator and denominator separately before dividing in expressions.

Evaluate \( \frac{x^2 + x - 20}{x + 5} \) when \( x = -2 \).

Learn how to evaluate the rational expression \( \frac{x^2 + x - 20}{x + 5} \) when \( x = -2 \) through a step-by-step solution. This problem covers key algebraic concepts, including substitution, simplification, and rational expressions. Suitable for students in Grades 8-10.

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