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To calculate \(\frac{f(x)}{g(x)}\), I will use the given functions:

1. \(f(x) = x^2 - 1\)
2. \(g(x) = x + 1\)

The division is straightforward:

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

### Simplification:
Using the difference of squares formula \(a^2 - b^2 = (a-b)(a+b)\):

\[
x^2 - 1 = (x - 1)(x + 1)
\]

Thus:

\[
\frac{f(x)}{g(x)} = \frac{(x - 1)(x + 1)}{x + 1}
\]

For \(x \neq -1\) (to avoid division by zero):

\[
\frac{f(x)}{g(x)} = x - 1
\]

### Final Result:
\[
\frac{f(x)}{g(x)} = x - 1 \quad \text{(for \(x \neq -1\))}.
\]

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Would you like me to evaluate this for specific values of \(x\) or explore any related operations?  

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### Related Questions:
1. What happens if \(x = -1\)?  
2. How do you compute \(\frac{f(x)}{g(x)}\) numerically for specific values of \(x\)?  
3. How would you graph \(\frac{f(x)}{g(x)}\) and identify asymptotes?  
4. Can you explore other combinations of \(f(x)\) and \(g(x)\) operations, such as \(f(x) \cdot g(x)\)?  
5. What is the domain of \(\frac{f(x)}{g(x)}\) and how does the function behave at boundaries?  

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### Tip:
Always check for restrictions in the domain (e.g., division by zero) when simplifying rational expressions!

Simplify the expression f(x) / g(x), given f(x) = x^2 - 1 and g(x) = x + 1.

Simplify the rational expression f(x)/g(x), where f(x) = x^2 - 1 and g(x) = x + 1. Explore the use of algebraic concepts such as factoring and rational function domain restrictions in this step-by-step solution. Suitable for Grades 9-10.

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