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The problem asks us to compute \( \left( \frac{f}{g} \right)(2) \), where:

\[
f(x) = x^3 - 2x - 3 \quad \text{and} \quad g(x) = 3x - 2.
\]

The function \( \frac{f}{g}(x) \) is defined as:

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

So, to compute \( \left( \frac{f}{g} \right)(2) \), we need to evaluate \( f(2) \) and \( g(2) \), then divide the results:

### Step 1: Compute \( f(2) \)
\[
f(2) = 2^3 - 2(2) - 3 = 8 - 4 - 3 = 1.
\]

### Step 2: Compute \( g(2) \)
\[
g(2) = 3(2) - 2 = 6 - 2 = 4.
\]

### Step 3: Compute \( \frac{f(2)}{g(2)} \)
\[
\frac{f(2)}{g(2)} = \frac{1}{4}.
\]

Thus, \( \left( \frac{f}{g} \right)(2) = \frac{1}{4} \).

Let me know if you need more details or have any other questions!

Here are 5 related questions for further practice:
1. What is \( f'(x) \) for \( f(x) = x^3 - 2x - 3 \)?
2. Find \( \left( \frac{f}{g} \right)'(2) \) for the given functions.
3. Compute \( \left( \frac{f}{g} \right)(-1) \) for the given functions.
4. If \( h(x) = f(x) \times g(x) \), what is \( h(2) \)?
5. Determine the zeroes of \( f(x) = x^3 - 2x - 3 \).

**Tip**: Always evaluate functions step by step to avoid confusion with algebraic manipulations!

Given: f(x) = x^3 - 2x - 3 and g(x) = 3x - 2. Find: (f/g)(2).

Explore how to calculate the value of (f/g)(2) when f(x) = x^3 - 2x - 3 and g(x) = 3x - 2. This example demonstrates evaluating polynomial functions and rational function operations, suitable for high school students learning advanced algebra.

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