Multiplying and Dividing Rational Expressions - Concept

Concept Concept (1)

Dividing rational expressions is basically two simplifying problems put together. When dividing rationals, we factor both numerators and denominators and identify equivalents of one to cancel. After identifying these equivalents, we take the reciprocal of the second fraction and divide. Multiplying rational expressions is the same as dividing rationals, except that we do not take the reciprocal of the second fraction.

Sample Sample Problems (9)

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Multiplying and Dividing Rational Expressions - Problem 1

Simplify:

x² + 3x + 2 x² + 7x + 12
x² + 4x + 3 x² − 4
Problem 1
How to multiply rational expressions involving quadratics.
Multiplying and Dividing Rational Expressions - Problem 2

Simplify:

y² − 4 ÷ 2 − y
16 8y
Problem 2
How to divide rational expressions involving an opposite.
Multiplying and Dividing Rational Expressions - Problem 3

Simplify:

( 2x³ + 3x² − 2x x² − 3x − 10 ) ÷ 3x² + 12x + 12
2x³ − x² 3x − 15 5x² − 10x
Problem 3
How to simplify a rational expression involving both multiplication and division.
Multiplying and Dividing Rational Expressions - Problem 4
Problem 4
Identifying domain restrictions of rational expressions.
Multiplying and Dividing Rational Expressions - Problem 5
Problem 5
Multiplying monomial rational expressions.
Multiplying and Dividing Rational Expressions - Problem 6
Problem 6
Multiplying polynomial rational expressions.
Multiplying and Dividing Rational Expressions - Problem 7
Problem 7
Dividing polynomial rational expressions.
Multiplying and Dividing Rational Expressions - Problem 8
Problem 8
Dividing monomial rational expressions.
Multiplying and Dividing Rational Expressions - Problem 9
Problem 9
Simplifying radical expressions by factoring and then crossing out common factors in top and bottom