If `g(x)=(x^(2)-4)/(x+2)` and `a=-5`, what is the value of `|g(a)|`?

Answer

To solve the problem, we need to find the value of \(|g(a)|\) where \(g(x) = \frac{x^2 - 4}{x + 2}\) and \(a = -5\).

### Step-by-Step Solution:

1. **Substitute \(a\) into \(g(x)\)**:
We need to find \(g(-5)\). So, we substitute \(-5\) into the function \(g(x)\):
\[ g(-5) = \frac{(-5)^2 - 4}{-5 + 2} \]

2. **Calculate the numerator**:
Calculate \((-5)^2 - 4\):
\[ (-5)^2 = 25 \quad \text{so} \quad 25 - 4 = 21 \]

3. **Calculate the denominator**:
Calculate \(-5 + 2\):
\[ -5 + 2 = -3 \]

4. **Combine the results**:
Now substitute the results back into the function:
\[ g(-5) = \frac{21}{-3} = -7 \]

5. **Find the absolute value**:
Now we need to find \(|g(-5)|\):
\[ |g(-5)| = |-7| = 7 \]

### Final Answer:
The value of \(|g(a)|\) is \(7\).