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The problem asks you to write the given expression as a single fraction and simplify it as much as possible. The expression is:

\[
\frac{t}{3} - \frac{t^2}{2u^2} \cdot \frac{-t}{u}
\]

### Step 1: Simplify the product of fractions
First, calculate the product of the second and third fractions:

\[
\frac{t^2}{2u^2} \cdot \frac{-t}{u} = \frac{-t^3}{2u^3}
\]

So the expression becomes:

\[
\frac{t}{3} - \frac{-t^3}{2u^3}
\]

This simplifies to:

\[
\frac{t}{3} + \frac{t^3}{2u^3}
\]

### Step 2: Combine into a single fraction
To combine these two fractions into one, find a common denominator. The common denominator between 3 and \(2u^3\) is \(6u^3\). Rewrite both fractions with this common denominator:

1. \(\frac{t}{3} = \frac{2t \cdot u^3}{6u^3}\)
2. \(\frac{t^3}{2u^3} = \frac{3t^3}{6u^3}\)

Now combine them:

\[
\frac{2tu^3 + 3t^3}{6u^3}
\]

### Final Answer:
The simplified expression is:

\[
\frac{2tu^3 + 3t^3}{6u^3}
\]

Would you like further details or explanations?

Here are some related questions:
1. How do you find a common denominator when adding fractions?
2. What is the importance of factoring in simplifying fractions?
3. How do you simplify complex fractions?
4. What is the difference between multiplying and adding fractions?
5. How can you check if a fraction is fully simplified?

**Tip:** Always check for common factors after combining fractions to simplify the expression further.

Schrijf als één breuk en vereenvoudig zo ver mogelijk: \frac{t}{3} - \frac{t^2}{2u^2} \cdot \frac{-t}{u}

Learn how to simplify the algebraic expression \frac{t}{3} - \frac{t^2}{2u^2} \cdot \frac{-t}{u} by combining fractions into a single fraction. This step-by-step solution covers key concepts like finding a common denominator and multiplying algebraic fractions, suitable for Grades 9-12.

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