Bruchterme & Bruchgleichungen: Understanding Fractional Terms and Equations

This page provides a comprehensive overview of fractional terms and equations, focusing on key concepts such as Definitionsmenge Bruchterme bestimmen and techniques for manipulating these expressions. The content is structured to help students grasp the fundamental principles of working with fractions in algebra.

Definition: Definitionsmenge (Domain) is the set of all numbers that can be substituted for the variable in a fractional term.

The page introduces the critical NNN-Rule (Nenner nie Null), which is essential for determining the domain of fractional expressions. This rule states that the denominator of a fraction must never be zero, which is crucial for avoiding undefined expressions.

Example: For the fraction x/(x-7), the domain is D={x ∈ Q | x ≠ 7} because when x = 7, the denominator would be zero, violating the NNN rule.

The document then delves into the techniques of expanding and simplifying fractional terms, which are fundamental skills for Bruchterme vereinfachen.

Highlight: Expanding fractional terms involves multiplying both the numerator and denominator by the same number or variable, while simplifying (kürzen) involves dividing both by a common factor.

Examples are provided for both numerical and algebraic fractions, demonstrating how to apply these techniques:

Example: Expanding 3/8 by multiplying both numerator and denominator by 2 results in 6/16.

Example: For algebraic fractions, expanding 4/(12y) by multiplying both parts by 3x yields (12x)/(36yx), with the condition that y ≠ 0 and x ≠ 0.

The page concludes with examples of simplifying fractional terms, reinforcing the concept of Bruchterme kürzen:

Example: Simplifying 15xy/(5x) results in 3y, with the condition that y ≠ 0.

This comprehensive guide provides students with a solid foundation for working with fractional terms and equations, emphasizing the importance of understanding domains and the rules governing fractional expressions in algebra.