To solve the equation:

\[
\frac{x-1}{x+5} = \frac{5}{3}
\]

### Step 1: Cross-multiply to eliminate the fractions.
\[
3(x-1) = 5(x+5)
\]

### Step 2: Expand both sides.
\[
3x - 3 = 5x + 25
\]

### Step 3: Move all terms involving \(x\) to one side and constants to the other side.
\[
3x - 5x = 25 + 3
\]
\[
-2x = 28
\]

### Step 4: Solve for \(x\).
\[
x = \frac{28}{-2} = -14
\]

So, the solution is:
\[
x = -14
\]

Would you like more details or have any other questions?

Here are 5 related questions:
1. What happens if \(x = -5\) in the original equation?
2. Can you solve for \(x\) if the right-hand side is a different fraction?
3. How would the equation change if the denominator was \(x - 5\)?
4. How do you solve equations with multiple fractions on both sides?
5. What if the original equation was squared on both sides?

**Tip:** Always check for extraneous solutions, especially when dealing with rational equations!

This detailed guide explains how to solve the rational equation (x-1)/(x+5) = 5/3 using cross multiplication. Learn step-by-step how to handle rational expressions, expand terms, and isolate variables. Suitable for students in Grades 8-10.

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