$$ \frac{5}{2 x-3}=\frac{3}{x+3} $$ Solve the equation. A. The solution set is $$ \{\square\} $$. (Simplify your answer.) B. There is no solution.

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{5}{2x - 3} = \frac{3}{x + 3}
$$

**Step 1: Cross-Multiply**

Multiply both sides of the equation by $$(2x - 3)(x + 3)$$ to eliminate the denominators:

$$
5(x + 3) = 3(2x - 3)
$$

**Step 2: Distribute**

Expand both sides:

$$
5x + 15 = 6x - 9
$$

**Step 3: Solve for $$x$$**

Subtract $$5x$$ from both sides:

$$
15 = x - 9
$$

Add $$9$$ to both sides:

$$
x = 24
$$

**Step 4: Check for Validity**

Ensure that the solution does not make any denominator zero:

- For $$2x - 3$$:
  
  $$
  2(24) - 3 = 48 - 3 = 45 \neq 0
  $$
  
- For $$x + 3$$:
  
  $$
  24 + 3 = 27 \neq 0
  $$

Since neither denominator is zero when $$x = 24$$, the solution is valid.

**Answer:**

**A. The solution set is $$ \{24\} $$.**
The solution is $$ x = 24 $$.

\[ \frac{5}{2 x-3}=\frac{3}{x+3} \] Solve the equation. A. The solution set is \( \{\square\} \). (Simplify your answer.) B. There is no solution.