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7'5 Complex Rational Expressions

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Complex Fractions ... Examples of complex fractions. Simplifying a Complex ... Multiply both the numerator and denominator of the complex fraction by the LCD. ... – PowerPoint PPT presentation

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Title: 7'5 Complex Rational Expressions


1
7.5 Complex Rational Expressions
To be able to work with complex rational
expressions, we should look back on the following
example
2
Complex Fractions
  • Complex rational expressions, also called complex
    fractions, have numerators or denominators
    containing one or more rational expressions.
  • Examples of complex fractions.

3
Simplifying a Complex Rational Expression by
Dividing
  • If necessary, add or subtract to get a single
    rational expression in the numerator.
  • If necessary, add or subtract to get a single
    rational expression in the denominator.
  • Perform the division indicated by the main
    fraction bar Invert the denominator of the
    complex rational expression and multiply.
  • If possible, simplify.

4
Simplifying a complex rational expression by
dividing.
The numerator is a single expression, so we do
nothing ?! Add to get a single expression in the
denominator. LCD is xy.
5
Simplifying a complex rational expression.
Invert and multiply. Simply.
6
Simplifying a Complex Rational Expression by
Multiplying by the LCD
  • Find the LCD of all rational expressions within
    the complex rational expression.
  • Multiply both the numerator and denominator of
    the complex fraction by the LCD.
  • Use the distributive property and multiply each
    term in the numerator and denominator by the LCD.
    Simplify. No fractional expressions should
    remain in the numerator and denominator.
  • If possible, factor and simplify.

7
Simplifying a complex rational expression by
multiplying.
Find the LCD of all rational expressions within
complex fraction. LCD 3xy
Multiply the numerator and denominator by the
LCD. Distribute the LCD.
Simplify.
8
7.5 Complex Rational Expressions
The notes for this section were based on the book
Blitzer, Introductory and Intermediate Algebra
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