1. **State the problem:** Simplify the expression $$\frac{1}{2+x} - \frac{2-x}{x}$$. 2. **Find a common denominator:** The denominators are $2+x$ and $x$. The common denominator is $$x(2+x)$$. 3. **Rewrite each fraction with the common denominator:** $$\frac{1}{2+x} = \frac{1 \cdot x}{(2+x) \cdot x} = \frac{x}{x(2+x)}$$ $$\frac{2-x}{x} = \frac{(2-x)(2+x)}{x(2+x)}$$ 4. **Expand the numerator of the second fraction:** $$(2-x)(2+x) = 2^2 + 2x - 2x - x^2 = 4 - x^2$$ 5. **Rewrite the expression:** $$\frac{x}{x(2+x)} - \frac{4 - x^2}{x(2+x)} = \frac{x - (4 - x^2)}{x(2+x)}$$ 6. **Simplify the numerator:** $$x - 4 + x^2 = x^2 + x - 4$$ 7. **Final simplified expression:** $$\frac{x^2 + x - 4}{x(2+x)}$$ **Answer:** $$\frac{x^2 + x - 4}{x(2+x)}$$