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The image shows a mathematical equation that needs to be solved. The equation is as follows:

\[
\frac{\frac{2}{3}}{x-1} = \frac{\frac{1}{2}}{x+3}
\]

Let's solve this equation step by step.

### Step 1: Simplify the fractions
Start by simplifying the fractions on both sides of the equation:

\[
\frac{2}{3(x-1)} = \frac{1}{2(x+3)}
\]

### Step 2: Cross multiply
To eliminate the fractions, cross multiply:

\[
2 \cdot 2(x + 3) = 3 \cdot 1(x - 1)
\]

This simplifies to:

\[
4(x + 3) = 3(x - 1)
\]

### Step 3: Expand both sides
Expand both sides of the equation:

\[
4x + 12 = 3x - 3
\]

### Step 4: Move terms involving \(x\) to one side
Subtract \(3x\) from both sides:

\[
x + 12 = -3
\]

### Step 5: Isolate \(x\)
Subtract 12 from both sides:

\[
x = -15
\]

### Final Answer
The solution to the equation is:

\[
x = -15
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you solve similar equations with variables in the denominator?
2. What are the rules for cross multiplying in an equation?
3. Can you explain the process of simplifying complex fractions?
4. What happens if the equation has no solution or infinite solutions?
5. How would this equation change if one side was squared?

### Tip:
Always check your solution by substituting it back into the original equation to verify it satisfies the equation.

Learn how to solve the equation (2/3) / (x-1) = (1/2) / (x+3) step-by-step with detailed explanations. This problem involves solving fractional equations and cross multiplication methods. Suitable for high school students.

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