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To solve this problem, let's break down the expression and simplify it:

The expression we need to simplify is:

\[
\frac{7x + 49}{x^2 + 2x - 35} \cdot \frac{x^2 - 25}{7x}
\]

### Step 1: Factor each term

1. **Numerator of the first fraction:** \(7x + 49\)
   - This can be factored as \(7(x + 7)\).

2. **Denominator of the first fraction:** \(x^2 + 2x - 35\)
   - This is a quadratic expression, and it factors as \((x + 7)(x - 5)\).

3. **Numerator of the second fraction:** \(x^2 - 25\)
   - This is a difference of squares, so it factors as \((x + 5)(x - 5)\).

4. **Denominator of the second fraction:** \(7x\) remains as it is.

### Step 2: Substitute the factored forms back into the expression

The expression now becomes:

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

### Step 3: Cancel common factors

1. The \(7\) in the numerator of the first fraction and the \(7\) in the denominator of the second fraction cancel each other.
2. The \((x + 7)\) term in the numerator of the first fraction and the denominator of the first fraction cancel each other.
3. The \((x - 5)\) term in the numerator of the second fraction and the denominator of the first fraction cancel each other.

After canceling, we are left with:

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

### Final Answer

The simplified form of the expression is:

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

So the correct answer is:

**D. \(\frac{x + 5}{x}\)**

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Would you like more details on any specific part of the solution, or do you have any questions?

Here are some related questions that may further enhance your understanding:

1. How do you factor quadratic expressions?
2. Why do factors cancel out in fractions?
3. What is the difference of squares, and how is it factored?
4. How do you determine the restrictions on variables in a rational expression?
5. What are common mistakes to avoid when simplifying complex fractions?

**Tip:** Always check for factors that can cancel out in both the numerator and the denominator to simplify expressions quickly.

Which expression is equivalent to \(\frac{7x + 49}{x^2 + 2x - 35} \cdot \frac{x^2 - 25}{7x}\)?

Learn how to simplify the rational expression \(\frac{7x + 49}{x^2 + 2x - 35} \cdot \frac{x^2 - 25}{7x}\) by factoring and canceling terms. This example includes factoring quadratics, using the difference of squares, and simplifying rational expressions. Ideal for students in Grades 9-10.

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