To solve the equation \(\frac{x-1}{x+1} = 5\), let's follow these steps:

1. Multiply both sides by \((x + 1)\) to eliminate the fraction:

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

2. Expand the right side:

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

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

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

   Simplify:

   \[
   -4x = 6
   \]

4. Divide by \(-4\) to solve for \(x\):

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

Thus, the solution is:

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

Would you like a detailed step-by-step explanation or have any questions?

Here are some related questions you might find helpful:

1. How would the solution change if the equation was \(\frac{x-1}{x+1} = -5\)?
2. What if the equation was \(\frac{x+1}{x-1} = 5\)?
3. How do you solve the equation \(\frac{2x-3}{x+4} = 7\)?
4. How would you solve \(\frac{x-1}{x+1} = \frac{3}{2}\)?
5. What are the implications if the denominator equals zero?

**Tip:** Always check for restrictions, such as values that make the denominator zero when solving rational equations.

Learn how to solve the rational equation (x-1)/(x+1) = 5 with a clear step-by-step approach. Understand key algebraic concepts like cross multiplication and solving linear equations. This guide is suitable for students in Grades 8-10.

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