1. **State the problem:** Simplify the expression $ \frac{2}{x} + \frac{x}{x+1} $. 2. **Find a common denominator:** The denominators are $ x $ and $ x+1 $. The common denominator is $ x(x+1) $. 3. **Rewrite each fraction with the common denominator:** $$ \frac{2}{x} = \frac{2(x+1)}{x(x+1)} $$ $$ \frac{x}{x+1} = \frac{x \cdot x}{(x+1) \cdot x} = \frac{x^2}{x(x+1)} $$ 4. **Add the fractions:** $$ \frac{2(x+1)}{x(x+1)} + \frac{x^2}{x(x+1)} = \frac{2(x+1) + x^2}{x(x+1)} $$ 5. **Expand the numerator:** $$ 2(x+1) + x^2 = 2x + 2 + x^2 $$ 6. **Write the final simplified expression:** $$ \frac{x^2 + 2x + 2}{x(x+1)} $$ This is the simplified form of the expression.