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The problem asks to subtract a rational function \( f(x) \) from an irrational function \( g(x) \), and it gives the following functions:

\[
f(x) = \frac{2x + 1}{x^2 - 4} \quad \text{and} \quad g(x) = \sqrt{x^2 + 1}
\]

You are asked to calculate \( (g - f)(x) \), which is the difference of these two functions:

\[
(g - f)(x) = g(x) - f(x)
\]

Substitute the given expressions for \( g(x) \) and \( f(x) \):

\[
(g - f)(x) = \sqrt{x^2 + 1} - \frac{2x + 1}{x^2 - 4}
\]

This is the final expression for \( (g - f)(x) \), which represents the subtraction of the two functions.

Would you like me to further simplify or explore specific properties of this function?

Here are 5 related questions to expand the topic:
1. What is the domain of \( (g - f)(x) \)?
2. Can you identify any points where \( (g - f)(x) \) is undefined?
3. How would you graph \( (g - f)(x) \)?
4. What happens to \( (g - f)(x) \) as \( x \) approaches infinity?
5. How can you approximate \( (g - f)(x) \) near \( x = 0 \)?

**Tip:** When combining rational and irrational functions, it's often useful to consider common domains and points of discontinuity carefully.

Restar una función racional de una irracional:
f(x) = (2x + 1) / (x^2 - 4) y g(x) = sqrt(x^2 + 1)
Calcular (g - f)(x).

Aprende a restar una función racional de una irracional resolviendo (g - f)(x), donde g(x) = sqrt(x^2 + 1) y f(x) = (2x + 1) / (x^2 - 4). Este problema cubre conceptos clave sobre funciones racionales e irracionales, adecuado para estudiantes de grados 10-12.

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