SUMMARY
The discussion focuses on the process of rationalizing the denominator of the complex fraction \(\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{5}}\). The user initially attempts to rationalize using the expression \(\frac{1}{(\sqrt{2} + \sqrt{3}) + \sqrt{5}} \cdot \frac{(\sqrt{2} + \sqrt{3}) - \sqrt{5}}{(\sqrt{2} + \sqrt{3}) - \sqrt{5}}\). After several calculations, the user questions the correctness of their solution compared to an answer book, which provides a different result: \(\frac{2\sqrt{3} + 3\sqrt{2} - \sqrt{30}}{12}\). Ultimately, the discussion clarifies the correct approach to rationalizing the denominator and confirms the validity of the user's steps.
PREREQUISITES
- Understanding of complex fractions
- Knowledge of rationalizing denominators
- Familiarity with square roots and their properties
- Basic algebraic manipulation skills
NEXT STEPS
- Study the method of rationalizing denominators in complex fractions
- Learn about simplifying expressions involving square roots
- Explore the use of conjugates in rationalization
- Practice problems involving rationalizing denominators with multiple square roots
USEFUL FOR
Students studying algebra, particularly those tackling complex fractions and rationalization techniques, as well as educators looking for examples to illustrate these concepts.