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The given expression is:

\[
\frac{x^2 - 6x + 9}{x^2 - 9} - 7
\]

We need to simplify this expression to find which of the provided options is equivalent. Let's break it down step by step.

1. **Factor the numerator and denominator** of the fraction:
   - The numerator \(x^2 - 6x + 9\) can be factored as \((x - 3)^2\).
   - The denominator \(x^2 - 9\) is a difference of squares and factors as \((x - 3)(x + 3)\).

Thus, the expression becomes:

\[
\frac{(x - 3)^2}{(x - 3)(x + 3)} - 7
\]

2. **Simplify the fraction**:
   Cancel out one factor of \((x - 3)\) in both the numerator and denominator:

\[
\frac{x - 3}{x + 3} - 7
\]

3. **Get a common denominator** to combine terms:

\[
\frac{x - 3}{x

Which expression is equivalent to the given expression?

Learn how to simplify rational expressions, like (x^2 - 6x + 9)/(x^2 - 9) - 7, by factoring the numerator and denominator and combining terms. This example demonstrates the use of the difference of squares formula and algebraic simplification techniques. Ideal for students in Grades 9-11.

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