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The question asks to "Select all rational functions" from the provided list. A rational function is a function that can be expressed as the ratio of two polynomials, where the denominator is not zero.

Let's analyze each option:

1. **A. \( m(x) = \frac{8x + 4}{8x^2 + 4x - 2} \)**  
   This is a rational function since both the numerator and denominator are polynomials.

2. **B. \( s(x) = \frac{\sqrt{8x^2 + 4x - 2}}{3 - 6x^2} \)**  
   This is not a rational function because the square root in the numerator disqualifies it from being a polynomial.

3. **C. \( b(x) = \frac{3x^2 + 4x - 2}{3 - 6x^2} \)**  
   This is a rational function since both the numerator and denominator are polynomials.

4. **D. \( r(x) = \frac{3x^2 + 4x - 2}{3 + |x|} \)**  
   This is not a rational function because the denominator involves an absolute value, which prevents it from being a polynomial.

5. **E. \( c(x) = \frac{8x^2 + 4x - 2}{3x + 1} \)**  
   This is a rational function since both the numerator and denominator are polynomials.

6. **F. \( h(x) = \frac{3}{3 + |x|} \)**  
   This is not a rational function due to the absolute value in the denominator.

7. **G. \( a(x) = \frac{8x^2 + 4x - 2}{3 - 6x^2} \)**  
   This is a rational function since both the numerator and denominator are polynomials.

8. **H. \( t(x) = \frac{8x^0.7 + 4x - 2}{3 - 6x^2} \)**  
   This is not a rational function because \( x^0.7 \) in the numerator is not a valid polynomial term.

9. **I. \( n(x) = \frac{8x^2 + 4x - 2}{3 - 6x^x} \)**  
   This is not a rational function because \( x^x \) in the denominator is not a polynomial expression.

### Conclusion:  
The correct rational functions are:
- A. \( m(x) = \frac{8x + 4}{8x^2 + 4x - 2} \)
- C. \( b(x) = \frac{3x^2 + 4x - 2}{3 - 6x^2} \)
- E. \( c(x) = \frac{8x^2 + 4x - 2}{3x + 1} \)
- G. \( a(x) = \frac{8x^2 + 4x - 2}{3 - 6x^2} \)

Do you have any questions or want further details? Here are some related questions:

1. What makes a function rational?
2. How do non-polynomial terms like square roots or absolute values disqualify a function as rational?
3. Can a function with a fractional exponent ever be a rational function?
4. What are the common types of discontinuities in rational functions?
5. How can we determine the domain of a rational function?

**Tip:** Always ensure both the numerator and denominator are polynomials when identifying rational functions.

Select all rational functions. There are several correct answers.

This problem asks students to identify rational functions from a list of given functions. Learn how to distinguish rational functions by understanding key algebraic concepts such as polynomials, square roots, and absolute values. Suitable for students in Grades 9-12.

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