� 𝑥 =
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2−1
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, when x = -0.6

To solve the expression \(\frac{x}{\frac{x^2 - 1}{x - 1}}\) when \(x = -0.6\), follow these steps:

1. **Substitute \(x = -0.6\) into the expression:**

   \[
   \frac{-0.6}{\frac{(-0.6)^2 - 1}{-0.6 - 1}}
   \]

2. **Calculate the square of \(-0.6\):**

   \[
   (-0.6)^2 = 0.36
   \]

3. **Substitute this value into the expression:**

   \[
   \frac{-0.6}{\frac{0.36 - 1}{-1.6}}
   \]

4. **Simplify the expression inside the fraction:**

   \[
   0.36 - 1 = -0.64
   \]

   So the expression becomes:

   \[
   \frac{-0.6}{\frac{-0.64}{-1.6}}
   \]

5. **Simplify the inner fraction:**

   \[
   \frac{-0.64}{-1.6} = 0.4
   \]

   So the expression is now:

   \[
   \frac{-0.6}{0.4}
   \]

6. **Finally, divide \(-0.6\) by \(0.4\):**

   \[
   \frac{-0.6}{0.4} = -1.5
   \]

Thus, when \(x = -0.6\), the expression evaluates to \(-1.5\).

Would you like further details or have any other questions? Here are some related questions to explore:

1. What happens to the expression if \(x = 0.5\)?
2. How would you simplify the expression for a general \(x\)?
3. What is the value of the expression when \(x = 1\)?
4. How does the expression behave as \(x\) approaches infinity?
5. Can the expression be factored or simplified further before substitution?
6. What is the significance of the points where the denominator becomes zero?
7. How does the sign of \(x\) affect the final result?
8. What are some applications of this type of rational expression in real-world problems?

**Tip:** Always check if the denominator becomes zero at any given value of \(x\), as this would make the expression undefined.

Learn how to solve the rational expression (x / ((x^2 - 1) / (x - 1))) when x = -0.6 with detailed step-by-step solution. This problem covers rational expressions, simplification techniques, and substitution method. Suitable for Grades 10-12.

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