We are given the equation:

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

To solve for \(x\), follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by \(x + 1\) to get rid of the denominator:

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

### Step 2: Distribute the 5 on the right-hand side

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

### Step 3: Move all terms involving \(x\) to one side
Subtract \(x\) from both sides:

\[
-1 = 4x + 5
\]

### Step 4: Isolate the \(x\) term
Subtract 5 from both sides:

\[
-1 - 5 = 4x
\]

\[
-6 = 4x
\]

### Step 5: Solve for \(x\)
Divide both sides by 4:

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

### Solution:
The value of \(x\) is \(-\frac{3}{2}\).

Would you like more details on any step, or have any questions?

Here are 5 related questions to explore further:

1. What if the equation was \(\frac{x - 2}{x + 2} = 5\)?
2. How would you solve \(\frac{x - 1}{x + 1} = -5\)?
3. What happens if the right-hand side of the equation was a fraction?
4. How can you verify the solution by substituting \(x = -\frac{3}{2}\) back into the original equation?
5. What if the denominator was a quadratic expression instead of linear?

**Tip:** Always check for extraneous solutions when dealing with equations that involve fractions or radicals.

Learn how to solve the linear equation (x-1)/(x+1) = 5 through a detailed, step-by-step solution. This example demonstrates cross-multiplication and solving for variables in algebraic fractions. Suitable for students in Grades 8-10.

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