### 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 Problems (9)

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Simplify:

 x² + 3x + 2 ⋅ x² + 7x + 12 x² + 4x + 3 x² − 4
###### Problem 1
How to multiply rational expressions involving quadratics.

Simplify:

 y² − 4 ÷ 2 − y 16 8y
###### Problem 2
How to divide rational expressions involving an opposite.

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.
###### Problem 4
Identifying domain restrictions of rational expressions.
###### Problem 5
Multiplying monomial rational expressions.
###### Problem 6
Multiplying polynomial rational expressions.
###### Problem 7
Dividing polynomial rational expressions.
###### Problem 8
Dividing monomial rational expressions.
###### Problem 9
Simplifying radical expressions by factoring and then crossing out common factors in top and bottom