To solve the equation:

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

Let's go through the steps:

### Step 1: Multiply both sides of the equation by \( x + 1 \) to eliminate the denominator:

\[
x - 1 = 5(x + 1)
\]

### Step 2: Expand the right-hand side:

\[
x - 1 = 5x + 5
\]

### Step 3: Move all the terms involving \( x \) to one side and the constants to the other:

\[
x - 5x = 5 + 1
\]

\[
-4x = 6
\]

### Step 4: Solve for \( x \) by dividing both sides by -4:

\[
x = \frac{6}{-4} = -\frac{3}{2}
\]

### Final Answer:
\[
x = -\frac{3}{2}
\]

Would you like further details on any of the steps?

Here are 5 related questions to practice:
1. Solve \( \frac{2x - 3}{x + 4} = 7 \).
2. Solve \( \frac{x + 2}{x - 3} = 4 \).
3. Solve \( \frac{3x - 5}{x + 2} = 6 \).
4. What happens if both sides of the equation are fractions?
5. How would you solve \( \frac{x + 1}{x - 1} = -2 \)?

**Tip**: When solving rational equations, always check for any restrictions on \( x \) that might make the denominator zero.

Discover how to solve the rational equation x-1/x+1 = 5 through a step-by-step breakdown. This problem emphasizes key algebraic techniques, including rational equation manipulation and cross multiplication, making it ideal for students in Grades 8-10.

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