https://file.aiquickdraw.com/mathbot/file/1725529881279wbr31cz2.jpg

The expression provided in the image is:

\[
\frac{\frac{5}{4}}{\left(\frac{3}{2} - \frac{1}{3}\right)}
\]

Let's break this down step by step:

### Step 1: Simplify the denominator
We need to subtract \(\frac{1}{3}\) from \(\frac{3}{2}\). To do this, we find a common denominator. The least common denominator between 2 and 3 is 6.

\[
\frac{3}{2} = \frac{9}{6}, \quad \frac{1}{3} = \frac{2}{6}
\]

Now, subtract:

\[
\frac{9}{6} - \frac{2}{6} = \frac{7}{6}
\]

### Step 2: Simplify the entire expression
Now, we have:

\[
\frac{\frac{5}{4}}{\frac{7}{6}}
\]

Dividing fractions is equivalent to multiplying by the reciprocal:

\[
\frac{5}{4} \times \frac{6}{7} = \frac{5 \times 6}{4 \times 7} = \frac{30}{28} = \frac{15}{14}
\]

Thus, the result of the expression is:

\[
\boxed{\frac{15}{14}}
\]

Would you like more details or have any further questions?

Here are five related questions for practice:
1. What is the result of \(\frac{\frac{7}{5}}{\frac{2}{3} + \frac{1}{4}}\)?
2. How do you simplify \(\frac{8}{3} \times \frac{5}{2}\)?
3. What is the least common denominator of \(\frac{5}{6}\) and \(\frac{3}{4}\)?
4. Solve the expression \(\frac{\frac{9}{8}}{\frac{7}{3} - \frac{5}{2}}\).
5. How do you divide two fractions like \(\frac{2}{5}\) and \(\frac{4}{7}\)?

**Tip:** When dividing fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal.

What is the result of the operation: \( \frac{\frac{5}{4}}{\left(\frac{3}{2} - \frac{1}{3}\right)} \)?

Learn how to simplify and solve the fraction expression \( \frac{5}{4} \div \left(\frac{3}{2} - \frac{1}{3}\right) \). This problem covers key concepts of fraction subtraction and division. Suitable for students in Grades 7-9.

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