Identify and explain the mistake in the following simplification. Then correctly simplify the first expression. x² + 2x - 24 2x+8 + x +3 || = x²+x-12 x- x +4 (x+4)(x-3) (x+4) (x+3)(x-3) x+3 x²+x-13 x + 3 x +3 + x- x +3 x-4 x +3 (cancel factor of 2 in first term) (factor numerator) (cancel factor of (x+4) and find LCD) (combine like terms in the sum)
Identify and explain the mistake in the following simplification. Then correctly simplify the first expression. x² + 2x - 24 2x+8 + x +3 || = x²+x-12 x- x +4 (x+4)(x-3) (x+4) (x+3)(x-3) x+3 x²+x-13 x + 3 x +3 + x- x +3 x-4 x +3 (cancel factor of 2 in first term) (factor numerator) (cancel factor of (x+4) and find LCD) (combine like terms in the sum)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Simplification Error Identification and Correction**
**Problem Statement:**
Identify and explain the mistake in the following simplification. Then correctly simplify the first expression.
**Given Expression:**
\[
\frac{x^2 + 2x - 24}{2x + 8} + \frac{x - 4}{x + 3}
\]
**Incorrect Simplification:**
\[
= \frac{x^2 + x - 12}{x + 4} + \frac{x - 4}{x + 3} \quad \text{(cancel factor of 2 in first term)}
\]
\[
= \frac{(x + 4)(x - 3)}{(x + 4)} + \frac{x - 4}{x + 3} \quad \text{(factor numerator)}
\]
\[
= \frac{(x + 3)(x - 3)}{x + 3} + \frac{x - 4}{x + 3} \quad \text{(cancel factor of (x+4) and find LCD)}
\]
\[
= \frac{x^2 + x - 13}{x + 3} \quad \text{(combine like terms in the sum)}
\]
**Explanation:**
The mistake occurs in the second line where the factor of 2 was incorrectly canceled from the first term. Proper simplification requires adjusting the expression by correctly factoring and combining terms without inappropriate cancellations.
**Correct Simplification:**
1. **Factor Completely:**
- Original terms should be factored fully without mishandling any coefficients such as 2.
2. **Find a Common Denominator:**
- Properly handle fractions by finding the least common denominator to combine expressions correctly.
3. **Combine Terms:**
- Ensure like terms are combined properly after applying the correct algebraic techniques.
This guide demonstrates the importance of verifying each step in algebraic simplifications to prevent errors, particularly when cancelling terms or factors, which is a common mistake in rational expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58479c98-79da-4f45-8dbf-3b0f01b3a5bd%2Fd256202b-f27d-4af9-ad56-951be6e18083%2Fusxyowp_processed.png&w=3840&q=75)
Transcribed Image Text:**Simplification Error Identification and Correction**
**Problem Statement:**
Identify and explain the mistake in the following simplification. Then correctly simplify the first expression.
**Given Expression:**
\[
\frac{x^2 + 2x - 24}{2x + 8} + \frac{x - 4}{x + 3}
\]
**Incorrect Simplification:**
\[
= \frac{x^2 + x - 12}{x + 4} + \frac{x - 4}{x + 3} \quad \text{(cancel factor of 2 in first term)}
\]
\[
= \frac{(x + 4)(x - 3)}{(x + 4)} + \frac{x - 4}{x + 3} \quad \text{(factor numerator)}
\]
\[
= \frac{(x + 3)(x - 3)}{x + 3} + \frac{x - 4}{x + 3} \quad \text{(cancel factor of (x+4) and find LCD)}
\]
\[
= \frac{x^2 + x - 13}{x + 3} \quad \text{(combine like terms in the sum)}
\]
**Explanation:**
The mistake occurs in the second line where the factor of 2 was incorrectly canceled from the first term. Proper simplification requires adjusting the expression by correctly factoring and combining terms without inappropriate cancellations.
**Correct Simplification:**
1. **Factor Completely:**
- Original terms should be factored fully without mishandling any coefficients such as 2.
2. **Find a Common Denominator:**
- Properly handle fractions by finding the least common denominator to combine expressions correctly.
3. **Combine Terms:**
- Ensure like terms are combined properly after applying the correct algebraic techniques.
This guide demonstrates the importance of verifying each step in algebraic simplifications to prevent errors, particularly when cancelling terms or factors, which is a common mistake in rational expressions.
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