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The given expression is:

\[
\frac{x^2 + 4x - 21}{x^2 - 8x + 15}
\]

After factoring, it simplifies to:

\[
\frac{(x + 7)(x - 3)}{(x - 5)(x - 3)}
\]

By canceling the common factor \((x - 3)\), the simplified expression is:

\[
\frac{x + 7}{x - 5}
\]

Thus, the correct option is:

\[
(x + 7)/(x - 5)
\]

Let me know if you need more details or have any questions!

Here are 5 related questions to further your understanding:
1. How do you determine common factors in a quadratic expression?
2. What is the significance of factoring in simplifying rational expressions?
3. Can any restrictions be placed on the values of \(x\) after simplification?
4. What if the quadratic expressions were not factorable? How would you simplify them then?
5. How does this technique extend to higher-degree polynomials?

**Tip:** Always check for values that make the denominator zero after simplifying. These are restrictions for the domain of the function.

Simplify the given expression: (x^2 + 4x - 21) / (x^2 - 8x + 15)

This example teaches how to simplify the rational expression (x^2 + 4x - 21) / (x^2 - 8x + 15) by factoring both the numerator and the denominator, and then canceling out the common factors. It covers essential algebraic concepts such as quadratic factoring and simplifying rational expressions. Suitable for Grades 9-11 students.

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