Answers: Arithmetic on algebraic fractions
These are the answers to Questions: Arithmetic on algebraic fractions.
Please attempt the questions before reading these answers!
Q1
1.1. \(\displaystyle \quad \dfrac{7}{x}\)
1.2. \(\displaystyle \quad \dfrac{2x-1}{3}\)
1.3. \(\displaystyle \quad \dfrac{3}{y}\)
1.4. \(\displaystyle \quad \dfrac{1}{x}\)
1.5. \(\displaystyle \quad -1\)
1.6. \(\displaystyle \quad \dfrac{3}{2x}\)
1.7. \(\displaystyle \quad \dfrac{7}{15y}\)
1.8. \(\displaystyle \quad \dfrac{x}{2}\)
1.9. \(\displaystyle \quad \dfrac{5x+2}{x(x+1)}\)
1.10. \(\displaystyle \quad \dfrac{6}{t-1}\)
1.11. \(\displaystyle \quad \dfrac{6}{x-3}\)
1.12. \(\displaystyle \quad \dfrac{x-6}{(x+2)(x-2)}\)
1.13. \(\displaystyle \quad \dfrac{3c+1}{c^2}\)
1.14. \(\displaystyle \quad \dfrac{x(2x-3)}{(x-3)(x+3)}\)
1.15. \(\displaystyle \quad \dfrac{x^2 - x - 5}{(x+2)^2}\)
Q2
2.1. \(\displaystyle \quad \dfrac{2x}{15}\)
2.2. \(\displaystyle \quad 6\)
2.3. \(\displaystyle \quad \dfrac{x(x+1)}{6}\)
2.4. \(\displaystyle \quad \dfrac{3}{4}\)
2.5. \(\displaystyle \quad \dfrac{x-3}{4}\)
2.6. \(\displaystyle \quad -\dfrac{6}{x}\)
2.7. \(\displaystyle \quad \dfrac{m}{2}\)
2.8. \(\displaystyle \quad \dfrac{x+2}{x+3}\)
2.9. \(\displaystyle \quad \dfrac{3}{4}\)
2.10. \(\displaystyle \quad \dfrac{x+3}{x+1}\)
2.11. \(\displaystyle \quad -\dfrac{3}{2}\)
2.12. \(\displaystyle \quad \dfrac{2x}{3(x-2)}\)
Q3
3.1. \(\displaystyle \quad \dfrac{5}{2}\)
3.2. \(\displaystyle \quad 6\)
3.3. \(\displaystyle \quad \dfrac{1}{2}\)
3.4. \(\displaystyle \quad \dfrac{3x}{2}\)
3.5. \(\displaystyle \quad \dfrac{4(x-2)}{3x}\)
3.6. \(\displaystyle \quad \dfrac{v-1}{v}\)
3.7. \(\displaystyle \quad -6\)
3.8. \(\displaystyle \quad 2\)
3.9. \(\displaystyle \quad \dfrac{1}{2}\)
3.10. \(\displaystyle \quad \dfrac{x+3}{x-3}\)
3.11. \(\displaystyle \quad 2\)
3.12. \(\displaystyle \quad \dfrac{3(x+2)}{2x}\)
Q4
4.1. \(\displaystyle \quad \dfrac{x+y}{y}\)
4.2. \(\displaystyle \quad -\dfrac{6x}{x+2}\)
4.3. \(\displaystyle \quad \dfrac{1}{2}\)
4.4. \(\displaystyle \quad \dfrac{t+2}{3t}\)
4.5. \(\displaystyle \quad -\dfrac{2x(x+1)}{x-1}\)
Version history and licensing
v1.0: initial version created 12/25 by Donald Campbell as part of a University of St Andrews VIP project.