We are asked to evaluate the expression:

\[
\frac{4a + 8b}{7 - a^2}
\]

with \( a = 3 \) and \( b = -1 \). Let's substitute these values into the expression:

\[
\frac{4(3) + 8(-1)}{7 - (3)^2}
\]

Now, simplify each part step by step:

- The numerator: \( 4(3) + 8(-1) = 12 - 8 = 4 \)
- The denominator: \( 7 - (3)^2 = 7 - 9 = -2 \)

So the expression becomes:

\[
\frac{4}{-2} = -2
\]

Thus, the value of the expression is \( -2 \).

Would you like more details or have any questions about the steps?

Here are 5 related questions to deepen understanding:

1. How would the expression change if \( b = 2 \) instead?
2. What happens to the denominator if \( a = -3 \)?
3. Can you derive a general formula for the expression in terms of \( a \) and \( b \)?
4. What does this expression represent graphically if plotted?
5. What happens if \( a = 0 \) and \( b = 1 \)?

**Tip:** When substituting values, always simplify the expression step by step to avoid mistakes.

Explore how to simplify the rational expression (4a + 8b) / (7 - a^2) when a = 3 and b = -1. This step-by-step solution demonstrates key algebraic techniques, including substitution and simplifying expressions, suitable for students in Grades 8-10.

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