https://r2.erweima.ai/mathbot/image/1726100847813tij1d8rt.jpg

Let's analyze the functions and solve the given problems based on the image provided. 

The problem defines three functions:

1. \( F(x) = 3x - 1 \)
2. \( h(x) = 5 - x \)
3. \( g(x) = \frac{x^2 - 1}{x} \)

You are asked to find the following:

### a) \( F(x) - g(x) \)

\[
F(x) - g(x) = (3x - 1) - \frac{x^2 - 1}{x}
\]
We'll simplify this expression step by step.

### b) \( h(x) + g(x) \)

\[
h(x) + g(x) = (5 - x) + \frac{x^2 - 1}{x}
\]
This also needs to be simplified.

Let's go ahead and compute these expressions. I will solve the algebra now.The simplified results for the expressions are:

### a) \( F(x) - g(x) \)
\[
F(x) - g(x) = 2x - 1 + \frac{1}{x}
\]

### b) \( h(x) + g(x) \)
\[
h(x) + g(x) = 5 - \frac{1}{x}
\]

Would you like to go over the steps in more detail, or do you have any further questions?

Here are five related questions to help you expand your understanding:

1. How would you compute \( F(x) \cdot g(x) \)?
2. What is the domain of the function \( g(x) = \frac{x^2 - 1}{x} \)?
3. Can you find the intersection points of \( F(x) \) and \( g(x) \)?
4. How does the behavior of \( g(x) \) change as \( x \) approaches zero?
5. How can you differentiate or integrate the function \( h(x) + g(x) \)?

**Tip:** When simplifying expressions with fractions, factor and combine terms carefully to avoid mistakes in algebra.

Find the expressions for F(x) - g(x) and h(x) + g(x), where F(x) = 3x - 1, h(x) = 5 - x, and g(x) = (x^2 - 1)/x.

Learn how to simplify function expressions with detailed solutions for F(x) - g(x) and h(x) + g(x), where F(x) = 3x - 1, h(x) = 5 - x, and g(x) = (x^2 - 1)/x. Suitable for high school students in Grade 11-12.

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