Page -2- Oxーy,4x+スxy 2x+Y ® 6x-11x+4. 2 9) 2 2x+5x-3 ソーメ A: 3x-4 A: Zx +y x+3 3: (6x-1)(x-4) (スx+3)(x-1) 3: -2x(x+y) スx(x+y) C: C. x-xー 2. %3D YーX D: D: NONE OF THESE NONE OF THESE
Page -2- Oxーy,4x+スxy 2x+Y ® 6x-11x+4. 2 9) 2 2x+5x-3 ソーメ A: 3x-4 A: Zx +y x+3 3: (6x-1)(x-4) (スx+3)(x-1) 3: -2x(x+y) スx(x+y) C: C. x-xー 2. %3D YーX D: D: NONE OF THESE NONE OF THESE
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![# Algebraic Expressions and Rationalizations
## Problem Set
### Problem 1:
**Simplify the expression:**
\((125x^{\frac{1}{2}}y^6)^{\frac{1}{3}}\)
- **Options:**
- A: \(\frac{125}{3}y^{\frac{6}{3}}\sqrt{x}\)
- B: \(5y^2\sqrt[3]{x}\)
- C: \(5x^{\frac{5}{6}}y\)
- D: **None of these**
### Problem 8:
**Evaluate the rational expression:**
\(\frac{6x^2 - 11x + 4}{2x^2 + 5x - 3}\)
- **Options:**
- A: \(\frac{3x - 4}{x + 3}\)
- B: \(\frac{(6x - 1)(x - 4)}{(2x + 3)(x - 1)}\)
- C: \(3x^2 - \frac{11}{5}x - \frac{4}{3}\)
- D: **None of these**
### Problem 9:
**Solve the expression:**
\(\frac{x^2 - y^2}{2x + y} \cdot \frac{4x + 2xy}{y - x}\)
- **Options:**
- A: \(2x + y\)
- B: \(-2x(x + y)\)
- C: \(\frac{2x(x + y)}{y - x}\)
- D: **None of these**
### Problem 10:
**Rationalize the denominator:**
\(\frac{4 - 3\sqrt{2}}{6 + \sqrt{2}}\)
- **Options:**
- A: \(\frac{15 - 11\sqrt{2}}{17}\)
- B: \(\frac{9 - 7\sqrt{2}}{19}\)
- C: \(-\frac{1}{4}\)
- D: **None of these**
### Problem 11:
**Evaluate the expression:**
\(\frac{2a^2 - ab - b^2}{6x^2 - x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c890fea-9ea3-43bb-93d7-8006a6dd7f77%2F25f7a271-bb99-44de-83df-196ad2c5b564%2Fmv22vbj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Algebraic Expressions and Rationalizations
## Problem Set
### Problem 1:
**Simplify the expression:**
\((125x^{\frac{1}{2}}y^6)^{\frac{1}{3}}\)
- **Options:**
- A: \(\frac{125}{3}y^{\frac{6}{3}}\sqrt{x}\)
- B: \(5y^2\sqrt[3]{x}\)
- C: \(5x^{\frac{5}{6}}y\)
- D: **None of these**
### Problem 8:
**Evaluate the rational expression:**
\(\frac{6x^2 - 11x + 4}{2x^2 + 5x - 3}\)
- **Options:**
- A: \(\frac{3x - 4}{x + 3}\)
- B: \(\frac{(6x - 1)(x - 4)}{(2x + 3)(x - 1)}\)
- C: \(3x^2 - \frac{11}{5}x - \frac{4}{3}\)
- D: **None of these**
### Problem 9:
**Solve the expression:**
\(\frac{x^2 - y^2}{2x + y} \cdot \frac{4x + 2xy}{y - x}\)
- **Options:**
- A: \(2x + y\)
- B: \(-2x(x + y)\)
- C: \(\frac{2x(x + y)}{y - x}\)
- D: **None of these**
### Problem 10:
**Rationalize the denominator:**
\(\frac{4 - 3\sqrt{2}}{6 + \sqrt{2}}\)
- **Options:**
- A: \(\frac{15 - 11\sqrt{2}}{17}\)
- B: \(\frac{9 - 7\sqrt{2}}{19}\)
- C: \(-\frac{1}{4}\)
- D: **None of these**
### Problem 11:
**Evaluate the expression:**
\(\frac{2a^2 - ab - b^2}{6x^2 - x
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