1. **Statement of the problem:** We need to determine if the function $$k(x) = \frac{(x^2)-4}{|x|-1}$$ is even. 2. **Recall the definition of an even function:** A function $$f(x)$$ is even if $$f(-x) = f(x)$$ for all $$x$$ in the domain. 3. **Calculate $$k(-x)$$:** $$k(-x) = \frac{((-x)^2)-4}{|-x|-1} = \frac{x^2 - 4}{|x| - 1}$$ 4. **Compare $$k(-x)$$ with $$k(x)$$:** Since $$k(x) = \frac{x^2 - 4}{|x| - 1}$$ and $$k(-x) = \frac{x^2 - 4}{|x| - 1}$$, we have $$k(-x) = k(x)$$. 5. **Conclusion:** The function $$k(x)$$ satisfies the condition for evenness, so $$k(x)$$ is an even function.