https://file.aiquickdraw.com/mathbot/file/1725935430184oz8veh1g.jpg

The given equation is:

\[
\frac{5}{x+2} = \frac{3}{x-2}
\]

To solve this, we can cross-multiply:

\[
5(x - 2) = 3(x + 2)
\]

Now, simplify both sides:

\[
5x - 10 = 3x + 6
\]

Next, collect like terms:

\[
5x - 3x = 6 + 10
\]

Simplify:

\[
2x = 16
\]

Solve for \(x\):

\[
x = \frac{16}{2} = 8
\]

Now, we check if this solution makes the denominators zero:

- For \(x + 2\), when \(x = 8\), it becomes \(8 + 2 = 10\), which is non-zero.
- For \(x - 2\), when \(x = 8\), it becomes \(8 - 2 = 6\), which is also non-zero.

Since there are no issues with division by zero, the solution is valid. Therefore, the solution set is:

\[
\{8\}
\]

The correct choice is **A**.

---

Would you like more details or have any questions?

Here are 5 related questions:
1. What would happen if one of the denominators had become zero?
2. How can you verify if a solution is extraneous?
3. How would the solution change if the equation was \(\frac{5}{x+2} = \frac{3}{x+1}\)?
4. What is cross-multiplication, and when is it used?
5. Can you solve rational equations with more complex expressions in the numerator?

**Tip:** Always check for restrictions in rational equations to avoid dividing by zero.

Solve the rational equation. If the equation has no solution, so state. 5/(x+2) = 3/(x-2)

Learn how to solve the rational equation 5/(x+2) = 3/(x-2) by cross-multiplying and simplifying. Check for any restrictions, such as division by zero, to ensure the solution is valid. Suitable for students in Grades 9-12.

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