SUMMARY
The expression sqrt(2)/(sqrt(2) - 1) simplifies to 2 + sqrt(2) through the use of the conjugate. By multiplying the numerator and denominator by the conjugate of the denominator, which is (sqrt(2) + 1), the expression can be rationalized. This technique eliminates the radical in the denominator, leading to the simplified form. The final result confirms the correctness of the simplification process.
PREREQUISITES
- Understanding of rationalizing denominators
- Knowledge of conjugates in algebra
- Familiarity with simplifying radical expressions
- Basic algebraic manipulation skills
NEXT STEPS
- Study the process of rationalizing denominators in algebra
- Learn about the properties and applications of conjugates
- Explore techniques for simplifying radical expressions
- Practice problems involving infinite series and their simplifications
USEFUL FOR
Students studying algebra, particularly those focusing on infinite series and simplification techniques, as well as educators looking for effective teaching methods in algebraic concepts.