Simplifying Rational Functions with Factoring and GCFs - Concept

Concept 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 Sample Problems (15)

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Simplifying Rational Functions with Factoring and GCFs - Problem 1

Simplify and find any excluded values.

4x³
16x
Problem 1
How to simplify rational expressions when there is a monomial common factor.
Simplifying Rational Functions with Factoring and GCFs - Problem 2

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.
Simplifying Rational Functions with Factoring and GCFs - Problem 3

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.
Simplifying Rational Functions with Factoring and GCFs - Problem 4

Simplify and find any excluded values.

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