The expression you've provided is:

\[
-3x^{-1} \cdot (6 + 2x)
\]

Let's simplify this step by step:

1. Recognize that \(x^{-1}\) is equivalent to \(\frac{1}{x}\).
   
   So the expression becomes:
   \[
   -3 \cdot \frac{1}{x} \cdot (6 + 2x)
   \]

2. Distribute \(-3 \cdot \frac{1}{x}\) to each term inside the parentheses:
   \[
   -3 \cdot \frac{1}{x} \cdot 6 + -3 \cdot \frac{1}{x} \cdot 2x
   \]

3. Simplify each term:
   - \(-3 \cdot \frac{1}{x} \cdot 6 = -\frac{18}{x}\)
   - \(-3 \cdot \frac{1}{x} \cdot 2x = -6\)

   Therefore, the simplified expression is:
   \[
   -\frac{18}{x} - 6
   \]

So, \(-3x^{-1} \cdot (6 + 2x)\) simplifies to:

\[
-\frac{18}{x} - 6
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What is the domain of the simplified expression?
2. How would the expression change if the coefficient \(-3\) were positive?
3. How would you differentiate the expression with respect to \(x\)?
4. What happens to the expression as \(x\) approaches zero?
5. How would the expression be affected if the \(x^{-1}\) term were replaced by \(x^{-2}\)?

**Tip:** When simplifying expressions, it's helpful to handle the distribution carefully and ensure each term is simplified independently before combining them.

Learn how to simplify the expression -3x^(-1) (6 + 2x) step-by-step. Understand the rules of exponents and distribution in algebraic simplification. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation