If `f(x) = x^(2)` and `g(x) = (1)/(x^(3))`. Then the value of `(f(x)+g(x))/(f(-x)-g(-x))` at `x = 2` is

Options

A. `(33)/(31)`
B. `(31)/(33)`
C. `1`
D. None of these

Explanation

To solve the problem, we need to evaluate the expression \((f(x) + g(x)) / (f(-x) - g(-x))\) at \(x = 2\), where \(f(x) = x^2\) and \(g(x) = \frac{1}{x^3}\).

### Step-by-Step Solution:

1. **Calculate \(f(2)\)**:
\[ f(2) = 2^2 = 4 \]

2. **Calculate \(g(2)\)**:
\[ g(2) = \frac{1}{2^3} = \frac{1}{8} \]

3. **Calculate \(f(-2)\)**:
\[ f(-2) = (-2)^2 = 4 \]

4. **Calculate \(g(-2)\)**:
\[ g(-2) = \frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8} \]

5. **Substitute values into the expression**:
\[ f(2) + g(2) = 4 + \frac{1}{8} = \frac{32}{8} + \frac{1}{8} = \frac{33}{8} \]
\[ f(-2) - g(-2) = 4 - \left(-\frac{1}{8}\right) = 4 + \frac{1}{8} = \frac{32}{8} + \frac{1}{8} = \frac{33}{8} \]

6. **Evaluate the final expression**:
\[ \frac{f(2) + g(2)}{f(-2) - g(-2)} = \frac{\frac{33}{8}}{\frac{33}{8}} = 1 \]

### Final Answer:
The value of \(\frac{f(x) + g(x)}{f(-x) - g(-x)}\) at \(x = 2\) is \(1\).