We are given the equation:

\[
\frac{5}{8} - \frac{3}{5} = \frac{x}{10}
\]

### Step 1: Find a common denominator for the fractions on the left-hand side.

The least common denominator (LCD) of \(8\) and \(5\) is \(40\). Let's rewrite each fraction with a denominator of 40:

\[
\frac{5}{8} = \frac{25}{40} \quad \text{and} \quad \frac{3}{5} = \frac{24}{40}
\]

Now, the equation becomes:

\[
\frac{25}{40} - \frac{24}{40} = \frac{x}{10}
\]

### Step 2: Subtract the fractions on the left-hand side.

\[
\frac{25}{40} - \frac{24}{40} = \frac{1}{40}
\]

Thus, the equation becomes:

\[
\frac{1}{40} = \frac{x}{10}
\]

### Step 3: Solve for \(x\).

To solve for \(x\), cross-multiply:

\[
1 \times 10 = 40 \times x
\]

\[
10 = 40x
\]

Now, divide both sides by 40:

\[
x = \frac{10}{40} = \frac{1}{4}
\]

Thus, the solution is:

\[
x = \frac{1}{4}
\]

Would you like further details on any of the steps?

Here are 5 related questions:
1. How do you find the least common denominator for different fractions?
2. What are the steps to simplify complex rational expressions?
3. How do you handle equations with multiple fractions on both sides?
4. Can you always cross-multiply when solving equations with fractions?
5. What are real-life applications of rational functions?

**Tip:** When working with fractions in an equation, always make sure to simplify the fractions before solving for the variable.

Discover how to solve the rational function 5/8 - 3/5 = x/10 using common denominators and cross-multiplication. This problem focuses on subtracting fractions and solving for variables in rational equations, perfect for students in Grades 6-8.

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