https://file.aiquickdraw.com/mathbot/file/1726165097860thpg1jbx.jpg

Looking at the problem presented in the image, Chuck is attempting to simplify the division of two rational expressions:

\[
\frac{x^2 + x - 6}{4x^6} \div \frac{x + 3}{2x^3}.
\]

### Step-by-step review of Chuck's work:
1. **Step 1:**
   Chuck factored \(x^2 + x - 6\) into \((x - 2)(x + 3)\), which is correct because:
   \[
   x^2 + x - 6 = (x - 2)(x + 3).
   \]
   However, Chuck seems to have prematurely written the entire expression for simplification without considering the division correctly yet.

2. **Step 2:**
   In this step, Chuck converted the division of fractions into multiplication by flipping the second fraction, which is correct. However, Chuck incorrectly canceled the factor \((x + 3)\) in both the numerator and denominator. The problem is that the denominator still contains \(4x^6\), and Chuck ignored this, leading to an erroneous cancellation.

3. **Step 3:**
   In the final step, Chuck wrote the simplified form as:
   \[
   \frac{x - 2}{2x^3}.
   \]
   The denominator should have been \(4x^6\), not \(2x^3\), meaning the simplification wasn't done correctly.

### The first mistake is in **Step 2**, where Chuck incorrectly crossed out the \((x + 3)\) factors, even though it wasn't completely factored out from both the numerator and denominator correctly.

### Correct Answer:
**b) On Step#2, Richard should have not crossed out the (x + 3) factors.**

---

Would you like further clarification or details? Here are 5 related questions:

1. How do you correctly divide rational expressions?
2. What is the proper way to factor quadratic expressions like \(x^2 + x - 6\)?
3. What are the common mistakes when simplifying rational expressions?
4. How do you cancel terms properly when simplifying rational expressions?
5. Why is flipping the second fraction necessary in division of fractions?

**Tip:** When simplifying rational expressions, always factor both the numerator and denominator completely before canceling terms.

Can you find the FIRST mathematical mistake Chuck made in his work when simplifying the expression \(\frac{x^2 + x - 6}{4x^6} \div \frac{x + 3}{2x^3}\)?

Review Chuck's work on dividing and simplifying rational expressions. Discover the first mistake made in crossing out terms incorrectly and learn the proper steps for simplifying. This problem is suitable for students in Grades 9-10, focusing on factoring, dividing rational expressions, and common simplification errors.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation