Lesson 8-1 : Multiplying and Dividing Rational Expressions
Rational Expression – A ratio of two polynomial expressions
To write a fraction in simplest form, you divide both the numerator and
the denominator, by the greatest common factor (GCF).
To simplify a rational expression, you use similar techniques.
Simplify:
Under what conditions is this expression undefined?
Sometimes you can factor out
in the numerator or denominator to
help simplify rational expressions.
Simplify by Factoring Out
Remember to:
Multiply two fractions, you multiply the numerators together and
the denominators together
Divide two fractions, you multiply by the reciprocal of the divisor.
The same procedures are used for multiplying and dividing rational
expressions.
Multiplying Rational Expressions
Multiply the numerators and denominators
Dividing Rational Expressions
Multiply by the reciprocal of the divisor
Multiply and Divide Rational Expressions
Ex.
Sometimes you must factor the numerator and/or the denominator
first before you can simplify a product or quotient of a rational
expression.
A Complex Fraction is a rational expression whose numerator and/or
denominator contain a rational expression.
To simplify a complex fraction, rewrite it as a division expression, and
use the rules for division.
Simplify a Complex Fraction
Ex.
Lesson 8-1 : Multiplying and Dividing Rational Expressions
Rational Expression – A ratio of two polynomial expressions
To write a fraction in simplest form, you divide both the numerator and the denominator, by the greatest
common factor (GCF).
To simplify a rational expression, you use similar techniques.
Simplify:
Under what conditions is this expression undefined?
Sometimes you can factor out
in the numerator or denominator to help simplify rational expressions.
Simplify by Factoring Out
Remember to:
Multiply two fractions, you multiply the numerators together and the denominators together
Divide two fractions, you multiply by the reciprocal of the divisor.
The same procedures are used for multiplying and dividing rational expressions.
Multiplying Rational Expressions
Multiply the numerators and denominators
Dividing Rational Expressions
Multiply by the reciprocal of the divisor
Multiply and Divide Rational Expressions
Ex.
Sometimes you must factor the numerator and/or the denominator first before you can simplify a product or
quotient of a rational expression.
A Complex Fraction is a rational expression whose numerator and/or denominator contain a rational
expression.
To simplify a complex fraction, rewrite it as a division expression, and use the rules for division.
Simplify a Complex Fraction
Ex.