### Concept (1)

Simplifying rational expressions combines everything learned about factoring common factors and polynomials. When simplifying rational functions, factor the numerator and denominator into terms multiplying each other and look for equivalents of one (something divided by itself). Include parenthesis around any expression with a "+" or "-" and if all terms cancel in the numerator, there is still a one there.

### Sample Problems (15)

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Simplify and find any excluded values.

4x³
16x
###### Problem 1
How to simplify rational expressions when there is a monomial common factor.

Simplify and find any excluded values.

18x³
6x + 12
###### Problem 2
How to simplify rational expressions when the numerator or denominator needs to be factored.

Simplify and find any excluded values.

8m + 16
2m² + 5m + 2
###### Problem 3
How to simplify rational expressions when both the numerator and denominator need to be factored.

Simplify and find any excluded values.

9 − 3x
3x² − 9 − 6x
###### Problem 4
How to simplify rational expressions when there are opposite factors.
###### Problem 5
Simplifying rational expressions with monomial greatest common factors.
###### Problem 6
Simplifying rational expressions using radical greatest common factors.
###### Problem 7
Rewriting rational expressions as separate fractions as a tool for simplifying.
###### Problem 8
Factoring with monomial greatest common factors to simplify rational expressions and find excluded values.
###### Problem 9
Factoring when "a" is not one to reduce rational expressions and find excluded values.
###### Problem 10
Factoring higher degree polynomials to reduce rational expressions and find excluded values.
###### Problem 11
Using opposite binomials to reduce rational expressions and find excluded values.
###### Problem 12
Addressing common errors in simplifying rational expressions.
###### Problem 13
Factoring numerators and denominators to reduce rational expressions and find excluded values.
###### Problem 14
Strategy for "clearing" complex, or double fractions where a sum or difference of fractions is embedded in another fraction.
###### Problem 15
Using opposite binomials to simplify rational expressions.