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The simplified equivalent forms of the given rational functions for \( x \neq 2 \) are:

1. For \( f(x) = \frac{x^3 - 2^3}{x - 2} \), the equivalent function is:
   \[
   f(x) = x^2 + 2x + 4
   \]

2. For \( g(x) = \frac{x^4 - 2^4}{x - 2} \), the equivalent function is:
   \[
   g(x) = (x + 2)(x^2 + 4)
   \]

Would you like further details or any additional questions?

Here are five related questions to explore:

1. How do you compute the limit of \( f(x) \) as \( x \to 2 \)?
2. Why is factoring useful in simplifying limits involving rational functions?
3. What happens if you directly substitute \( x = 2 \) into \( f(x) \) and \( g(x) \)?
4. How would you use L'Hopital's Rule to evaluate these limits?
5. Can these rational functions have any other points of indeterminacy?

**Tip:** Always check for common factors in rational functions to simplify them before calculating limits.

Evaluate the limits of rational functions f(x) and g(x) as x approaches 2, and provide the simplified equivalent forms for x ≠ 2.

Learn how to evaluate the limits of rational functions as x approaches 2 by simplifying using factoring. This problem explores key calculus concepts, including the limit of f(x) and g(x) when x ≠ 2.

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