The given equation is:

\[
\frac{3x}{5x} + 2 = -4
\]

### Step 1: Simplify the term \(\frac{3x}{5x}\)
Since both the numerator and denominator contain \(x\), they cancel each other out:

\[
\frac{3x}{5x} = \frac{3}{5}
\]

So the equation becomes:

\[
\frac{3}{5} + 2 = -4
\]

### Step 2: Subtract 2 from both sides

\[
\frac{3}{5} = -4 - 2
\]

\[
\frac{3}{5} = -6
\]

### Step 3: Multiply both sides by 5 to eliminate the denominator

\[
3 = -6 \times 5
\]

\[
3 = -30
\]

This is a contradiction, meaning there is no solution to this equation.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you solve rational equations?
2. What happens when an equation results in a contradiction?
3. How can we solve equations with fractions?
4. What is the process to simplify terms like \(\frac{3x}{5x}\)?
5. How can we check for solutions after solving equations?

**Tip:** Always simplify both sides of an equation fully to catch potential contradictions early on.

Learn how to solve the rational equation 3x/5x + 2 = -4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations with fractions and rational equations. Suitable for students in Grades 9-12.

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