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To solve the problem, we need to find the formula for the composite function \( \frac{f}{g}(x) \), where \( f(x) = x + 1 \) and \( g(x) = x^2 - 1 \). Here are the steps:

### Step 1: Understand the function
The division of two functions \( \frac{f}{g}(x) \) is defined as:
\[
\frac{f}{g}(x) = \frac{f(x)}{g(x)}
\]

### Step 2: Substitute \( f(x) \) and \( g(x) \)
Given:
\[
f(x) = x + 1, \quad g(x) = x^2 - 1
\]
Substitute these into the formula:
\[
\frac{f}{g}(x) = \frac{x + 1}{x^2 - 1}
\]

### Step 3: Simplify the denominator
Note that \( x^2 - 1 \) can be factored as a difference of squares:
\[
x^2 - 1 = (x - 1)(x + 1)
\]
Thus:
\[
\frac{f}{g}(x) = \frac{x + 1}{(x - 1)(x + 1)}
\]

### Step 4: Simplify the fraction
Cancel \( x + 1 \) in the numerator and denominator, provided \( x \neq -1 \) (to avoid division by zero):
\[
\frac{f}{g}(x) = \frac{1}{x - 1}, \quad x \neq -1
\]

### Final Answer:
The formula for \( \frac{f}{g}(x) \) is:
\[
\frac{f}{g}(x) = \frac{1}{x - 1}, \quad x \neq -1
\]

Would you like a detailed breakdown of this explanation or have any questions?

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Here are 5 related questions:
1. How do you handle undefined points in a function, such as \( x = -1 \) in this case?
2. What is the domain of \( \frac{f}{g}(x) \) given this solution?
3. How would this change if \( f(x) = x^2 + 2x + 1 \)?
4. What happens if \( g(x) \) has a repeated factor in its denominator?
5. How can this concept be extended to division of more complex functions?

**Tip:** Always check for restrictions in the domain, especially where the denominator equals zero.

Diketahui f(x) = x + 1 dan g(x) = x^2 - 1. Rumus fungsi (f/g)(x) adalah ....

Learn how to simplify the rational function (f/g)(x) when f(x) = x + 1 and g(x) = x^2 - 1. This step-by-step solution covers function operations, factoring, and domain restrictions. Ideal for high school students studying algebra.

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