https://file.aiquickdraw.com/mathbot/file/1726834945888vdht8xse.jpg

The expression in the image appears to represent the following:

\[
\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{ab}}
\]

Let's break this down and simplify it step-by-step.

1. **Step 1: Simplify the numerator**
   \[
   \frac{1}{a} + \frac{1}{b} = \frac{b}{ab} + \frac{a}{ab} = \frac{a + b}{ab}
   \]

2. **Step 2: Now substitute this into the original expression**
   \[
   \frac{\frac{a + b}{ab}}{\frac{1}{ab}}
   \]

3. **Step 3: Simplify the fraction by multiplying by the reciprocal**
   \[
   \frac{a + b}{ab} \times \frac{ab}{1} = a + b
   \]

Thus, the entire expression simplifies to:

\[
a + b
\]

Would you like more details on any part of the solution? Here are a few related questions to expand your understanding:

1. How would this expression change if you had different denominators in the first step?
2. How does the simplification process differ when there are more terms in the numerator?
3. Can you express the same idea for a similar structure with variables like \(\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{xy}}\)?
4. How do you simplify complex rational expressions in general?
5. What would happen if one of the variables (like \(a\) or \(b\)) were zero in this expression?

**Tip:** When simplifying fractions within fractions (complex fractions), remember to combine the terms in the numerator first and then multiply by the reciprocal of the denominator.

Simplify the expression \( \frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{ab}} \)

Learn how to simplify the complex fraction \( \frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{ab}} \) with a step-by-step solution. This algebraic problem covers rational expressions, combining fractions, and reciprocal multiplication. Suitable for students in Grades 7-9.

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