To find the function \(\left(\frac{f}{g}\right)(x)\), you need to divide the two given functions:

\[
\left(\frac{f}{g}\right)(x) = \frac{\frac{3x+1}{x^2-25}}{\frac{2x-4}{x^2-25}}
\]

When dividing fractions, you multiply the numerator by the reciprocal of the denominator. So, this becomes:

\[
\left(\frac{f}{g}\right)(x) = \frac{3x+1}{x^2-25} \times \frac{x^2-25}{2x-4}
\]

Since the \(x^2 - 25\) terms in the numerator and denominator are the same, they cancel out, simplifying to:

\[
\left(\frac{f}{g}\right)(x) = \frac{3x + 1}{2x - 4}
\]

This is the simplified form of the function \(\left(\frac{f}{g}\right)(x)\).

### Do you want details or have any questions?

### Related Questions:
1. What are the domain restrictions for \(\left(\frac{f}{g}\right)(x)\)?
2. How do you factor the expression \(2x - 4\)?
3. Can \(\left(\frac{f}{g}\right)(x)\) be simplified further?
4. How would you find the roots of the numerator and denominator separately?
5. How would you find the inverse of \(\left(\frac{f}{g}\right)(x)\)?

**Tip:** Always check the domain restrictions after simplifying, especially in rational functions, to avoid division by zero.

Learn how to simplify the rational function (f/g)(x) = (3x+1)/(x^2-25) / (2x-4)/(x^2-25) step-by-step with detailed explanations. This problem involves rational functions, fractions simplification, and division of functions, suitable for students in Grades 10-12.

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