6.4 Complex fractions
Unit 6 · Rational expressions and functions
Ideas in this lesson
Simplify smaller fractions
Simplify the numerator and denominator of a complex fraction separately before dividing.
Use a reciprocal
A complex fraction represents division. Invert the entire denominator and multiply.
Clear smaller denominators
Multiply the entire numerator and denominator by the LCD of the smaller fractions.
State all restrictions
Keep restrictions from the smaller denominators and from requiring the entire denominator of the complex fraction to be nonzero.
Negative exponents and nested complex fractions, with stated nonzero assumptions
negative exponents and nested complex fractions, with stated nonzero assumptions.
Derive/simplify reciprocal physical models such as parallel resistance or a lens-style abstract reciprocal relationship; retain units and realistic domains
derive/simplify reciprocal physical models such as parallel resistance or a lens-style abstract reciprocal relationship; retain units and realistic domains.
Prove two parameterized formulas equivalent (including the algebraic structure of the source payment formula) with explicit denominator and parameter restrictions
prove two parameterized formulas equivalent (including the algebraic structure of the source payment formula) with explicit denominator and parameter restrictions.
Continue and simplify a finite continued-fraction pattern and explain its numerical trend; distinguish a conjectured limit from a proved limit
continue and simplify a finite continued-fraction pattern and explain its numerical trend; distinguish a conjectured limit from a proved limit.
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