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The given expression is:

\[
\frac{\frac{5}{z} \times \frac{2}{x}}{\frac{4}{z} \times \frac{6}{x}}
\]

We can simplify this step by step:

### Step 1: Simplify the numerator
The numerator is \(\frac{5}{z} \times \frac{2}{x}\), which is simply:

\[
\frac{5 \times 2}{z \times x} = \frac{10}{zx}
\]

### Step 2: Simplify the denominator
The denominator is \(\frac{4}{z} \times \frac{6}{x}\), which is:

\[
\frac{4 \times 6}{z \times x} = \frac{24}{zx}
\]

### Step 3: Simplify the whole expression
Now the overall expression becomes:

\[
\frac{\frac{10}{zx}}{\frac{24}{zx}} = \frac{10}{24}
\]

### Step 4: Simplify the fraction
\[
\frac{10}{24} = \frac{5}{12}
\]

Thus, the simplified expression is:

\[
\frac{5}{12}
\]

Let me know if you would like further details!

### Related Questions:
1. How do you multiply and divide fractions involving variables?
2. What are the properties of fractions when multiplying and dividing?
3. How can you simplify expressions with variables in both the numerator and denominator?
4. How do you reduce a fraction to its simplest form?
5. What are common mistakes to avoid when simplifying algebraic fractions?

**Tip:** When simplifying expressions with multiple variables, factor out common terms between the numerator and the denominator to make simplification easier.

Simplify the expression \( \frac{\frac{5}{z} \times \frac{2}{x}}{\frac{4}{z} \times \frac{6}{x}} \)

Learn how to simplify the expression \( \frac{\frac{5}{z} \times \frac{2}{x}}{\frac{4}{z} \times \frac{6}{x}} \) step by step. This problem covers key algebraic concepts, including the multiplication and simplification of fractions with variables in both the numerator and denominator. Suitable for students in Grades 7-9.

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