Answers: Introduction to algebraic fractions
These are the answers to Questions: Introduction to algebraic fractions.
Please attempt the questions before reading these answers!
Q1
1.1. \(\displaystyle \quad x \neq 0\)
1.2. \(\displaystyle \quad x \neq 4\)
1.3. \(\displaystyle \quad x \neq -\dfrac{1}{2}\)
1.4. \(\displaystyle \quad y \neq -5\)
1.5. \(\displaystyle \quad x \neq 0\) and \(x \neq \dfrac{2}{3}\)
1.6. \(\displaystyle \quad t \neq -2\) and \(t \neq 3\)
1.7. \(\displaystyle \quad x \neq -4\) and \(x \neq 4\)
1.8. \(\displaystyle \quad x \neq 1\)
1.9. \(\displaystyle \quad b \neq -4\) and \(b \neq 0\)
1.10. \(\displaystyle \quad x \neq -3\) and \(x \neq \dfrac{5}{2}\)
1.11. \(\displaystyle \quad x \neq 2\) and \(x \neq 3\)
1.12. \(\displaystyle \quad z \neq -4\) and \(z \neq 2\)
Q2
2.1. \(\displaystyle \quad 3x\)
2.2. \(\displaystyle \quad 5t\)
2.3. \(\displaystyle \quad 3a + 3\)
2.4. \(\displaystyle \quad 12x\)
2.5. \(\displaystyle \quad 10\)
2.6. \(\displaystyle \quad 2t - 6\)
2.7. \(\displaystyle \quad 3y - 3\)
2.8. \(\displaystyle \quad 3x\)
2.9. \(\displaystyle \quad 6x\)
2.10. \(\displaystyle \quad 6z - 3\)
2.11. \(\displaystyle \quad x(x+1)\)
2.12. \(\displaystyle \quad r^2 + r - 6\)
2.13. \(\displaystyle \quad 4x(x+1)\)
2.14. \(\displaystyle \quad 3x - 15\)
2.15. \(\displaystyle \quad 2z - 10\)
Q3
3.1. \(\displaystyle \quad \dfrac{2}{3}\) if \(y\neq 0\)
3.2. \(\displaystyle \quad \dfrac{x}{3}\) if \(x\neq 0\)
3.3. \(\displaystyle \quad n + 4\) if \(n\neq 0\)
3.4. \(\displaystyle \quad \dfrac{x-3}{2}\) if \(x\neq 0\)
3.5. \(\displaystyle \quad -\dfrac{2}{5}\) if \(x\neq 0\)
3.6. \(\displaystyle \quad m + 4\) if \(m\neq 4\)
3.7. \(\displaystyle \quad x - 1\) if \(x\neq -1\)
3.8. \(\displaystyle \quad x + 3\) if \(x\neq -2\)
3.9. \(\displaystyle \quad z + 5\) if \(z\neq 2\)
3.10. \(\displaystyle \quad 2x + 1\) if \(x\neq -3\)
3.11. \(\displaystyle \quad y - 5\) if \(y\neq 5\)
3.12. \(\displaystyle \quad -1\) if \(x\neq 4\)
3.13. \(\displaystyle \quad 2\) if \(x\neq -2\) and \(x \neq 2\)
3.14. \(\displaystyle \quad c\) if \(c\neq -2\) and \(c \neq 2\)
3.15. \(\displaystyle \quad \dfrac{A+2}{A+5}\) if \(A\neq -5\) and \(A \neq 5\)
Version history and licensing
v1.0: initial version created 12/25 by Donald Campbell as part of a University of St Andrews VIP project.