The expression you've written can be understood as:

\[
\frac{\frac{1}{m^3} + a^3}{\frac{1}{m^2} - a^2}
\]

Let's simplify this step by step:

### 1. Simplifying the numerator:
\[
\frac{1}{m^3} + a^3
\]
This is already simplified.

### 2. Simplifying the denominator:
\[
\frac{1}{m^2} - a^2
\]
You can factor \(a^2\) as:
\[
\frac{1}{m^2} - a^2 = \frac{1}{m^2} - \left(\frac{a}{1}\right)^2
\]
This is a difference of squares, which factors as:
\[
\left(\frac{1}{m} - a\right)\left(\frac{1}{m} + a\right)
\]

### 3. Final expression:
Now, rewrite the full expression:
\[
\frac{\frac{1}{m^3} + a^3}{\left(\frac{1}{m} - a\right)\left(\frac{1}{m} + a\right)}
\]

This is the simplified form of your original expression. It cannot be simplified further without specific values for \(m\) and \(a\).

Do you need further explanation or have any specific questions?

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Here are five related questions:
1. How do you factor expressions involving cubes?
2. Can this expression be simplified further for specific values of \(m\) and \(a\)?
3. What are the rules for simplifying fractions involving variables?
4. How do you simplify complex rational expressions?
5. What is the difference between factoring squares and cubes?

**Tip:** When simplifying complex rational expressions, always look for factoring opportunities like differences of squares or cubes.

Learn how to simplify the rational expression 1/m^3 + a^3 divided by 1/m^2 - a^2. This solution involves factoring techniques, including the difference of squares and cubes. Suitable for students in Grades 10-12, this step-by-step explanation covers key algebraic concepts in rational expressions.

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