Let's solve the equation:

\[
\frac{5m + 3n}{5m - 3n} = 7
\]

### Step 1: Multiply both sides of the equation by \(5m - 3n\) to eliminate the denominator:
\[
5m + 3n = 7(5m - 3n)
\]

### Step 2: Expand the right-hand side:
\[
5m + 3n = 35m - 21n
\]

### Step 3: Rearrange all terms involving \(m\) on one side and those involving \(n\) on the other:
\[
5m - 35m = -21n - 3n
\]

### Step 4: Simplify both sides:
\[
-30m = -24n
\]

### Step 5: Divide both sides by \(-30\):
\[
m = \frac{24n}{30}
\]

### Step 6: Simplify the fraction:
\[
m = \frac{4n}{5}
\]

So, the solution is:

\[
m = \frac{4n}{5}
\]

If you'd like any further details or have questions, feel free to ask!

Here are 5 related questions for you to try:
1. Solve \(\frac{7x + 2y}{7x - 2y} = 5\).
2. If \( m = \frac{4n}{5} \), what is the value of \(m\) when \(n = 10\)?
3. Rearrange the equation \(\frac{3a + 4b}{3a - 4b} = 6\) and solve for \(a\).
4. Solve \(\frac{9p + q}{9p - q} = 8\) for \(p\).
5. Solve for \(x\): \(\frac{2x + 6}{2x - 6} = 9\).

**Tip**: Always isolate the variable you're solving for by first clearing any fractions in the equation!

Learn how to solve the rational equation (5m + 3n) / (5m - 3n) = 7 with a clear, step-by-step solution. This problem demonstrates key algebraic concepts such as variable isolation, multiplying through denominators, and simplifying terms. Perfect for students in Grades 8-10.

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