O A B C D x+1 3 x³ +6x² 3x² X3 4x-16 x²-2x-8 x+5 = 1 2x² + 3x 2x²+5x+3 = = 4 x+4 = x² X
O A B C D x+1 3 x³ +6x² 3x² X3 4x-16 x²-2x-8 x+5 = 1 2x² + 3x 2x²+5x+3 = = 4 x+4 = x² X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
After Removing any discontinuities, which of these examples is a rational equation with extraneous solution?

![Below are the transcriptions of the mathematical equations as they might appear on an educational website. The answer options appear to be in a multiple-choice format for solving rational equations:
**Option A:**
\[
\frac{x+1}{3} = \frac{x+5}{x}
\]
**Option B:**
\[
\frac{x^3 + 6x^2}{3x^2} = 1
\]
**Option C:**
\[
\frac{4x - 16}{x^2 - 2x - 8} = \frac{4}{x+4}
\]
**Option D:**
\[
\frac{2x^2 + 3x}{2x^2 + 5x + 3} = x^2 - x
\]
### Additional Explanation
- **Option A** involves solving a fractional equation with variables in both the numerator and denominator on each side.
- **Option B** simplifies a rational expression to test whether it is equal to 1.
- **Option C** requires finding equivalence between two rational expressions featuring polynomials.
- **Option D** connects a rational expression with a polynomial expression on the right side.
The selected option with the blue dot is **Option C**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17a2d8ab-b196-429b-9620-8f2501e2e071%2Fc452d69c-2f16-45a8-9079-081bc37a2d85%2Fphct6a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Below are the transcriptions of the mathematical equations as they might appear on an educational website. The answer options appear to be in a multiple-choice format for solving rational equations:
**Option A:**
\[
\frac{x+1}{3} = \frac{x+5}{x}
\]
**Option B:**
\[
\frac{x^3 + 6x^2}{3x^2} = 1
\]
**Option C:**
\[
\frac{4x - 16}{x^2 - 2x - 8} = \frac{4}{x+4}
\]
**Option D:**
\[
\frac{2x^2 + 3x}{2x^2 + 5x + 3} = x^2 - x
\]
### Additional Explanation
- **Option A** involves solving a fractional equation with variables in both the numerator and denominator on each side.
- **Option B** simplifies a rational expression to test whether it is equal to 1.
- **Option C** requires finding equivalence between two rational expressions featuring polynomials.
- **Option D** connects a rational expression with a polynomial expression on the right side.
The selected option with the blue dot is **Option C**.
Expert Solution
Step 1
Extraneous Solution simply means a solution that comes out in solving process but does not satisfy the equation.
Step by step
Solved in 2 steps with 1 images
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