1. The problem is to understand whether it is correct to put $\frac{1}{a}$ and $\frac{1}{b}$ together as $\frac{1}{a} + \frac{1}{b}$ or in some other form. 2. The formula for adding fractions with different denominators is: $$\frac{1}{a} + \frac{1}{b} = \frac{b}{ab} + \frac{a}{ab} = \frac{a+b}{ab}$$ 3. Important rule: You cannot simply add the denominators when adding fractions. You must find a common denominator, which is the product of the denominators if they are different. 4. Step-by-step: - Start with $\frac{1}{a} + \frac{1}{b}$. - Find common denominator $ab$. - Rewrite each fraction: $\frac{1}{a} = \frac{b}{ab}$ and $\frac{1}{b} = \frac{a}{ab}$. - Add numerators: $\frac{b}{ab} + \frac{a}{ab} = \frac{a+b}{ab}$. 5. Therefore, $\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$. 6. This shows you should not just put $\frac{1}{a}$ and $\frac{1}{b}$ together without finding a common denominator and adding properly. Final answer: $$\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$$