Complex Mathematical Operations and Fractions

This comprehensive page covers essential mathematical operations involving fractions, algebraic expressions, and complex equations. The content is structured with multiple examples and detailed solutions to facilitate understanding.

Definition: Complex fractions are mathematical expressions where either the numerator or denominator (or both) contain fractions themselves.

Example: The solution process for example 87 demonstrates fraction multiplication:

(axc)/(bxf) = (a-c)/b × (a+c)/b

Highlight: Special attention is given to the proper handling of variables in fractional expressions, particularly when dealing with operations like multiplication and division.

Vocabulary: Key mathematical terms introduced include:

• Numerator: The top part of a fraction
• Denominator: The bottom part of a fraction
• Complex fraction: A fraction containing other fractions

Example: A practical application is shown in example 84:

(3x² + 8x³)/(3x² - 4 - 8) = 18/12 = 3/2

The page concludes with additional practice problems and examples numbered 13 through 15, providing students with opportunities to apply the concepts learned.