Definitions:

A rational expression is the ratio of two polynomials.

If f is a rational expression then f can be written in the form p/q where p and q are polynomials. Like polynomials or any other type of expression, the basic arithmetic operations, namely addition, subtraction, multiplication, and division, can be performed on rational expressions. A nice property of rational expressions is that when any of these operations are performed on two rational expressions, the result is always another rational expression. Contrary to polynomials, it is generally easy to multiply or divide but difficult to add or subtract two rational expressions.

To simplify a rational expression: $$\frac{x^2-16}{x^3+64}$$ a) Completely factor numerators and denominators. $$\frac{(x+4)(x-4)}{(x+4)(x^2-4x+16)}$$ b) Reduce common factors. $$\frac{(x-4)}{(x^2-4x+16)}$$

Rational equations can be used to solve a variety of problems that involve rates, times and work. Using rational expressions and equations can help us answer questions about how to combine workers or machines to complete a job on schedule.

Simplifying Rational Expressions Introduction

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Length: 15:23

Factoring quadratic expressions

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Length: 16:30

Subtracting Rational Expressions

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Length: 5:35

Multiplying and Simplifying Rational Expressions

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Length: 5:05

Example 1: Factoring difference of squares

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Length: 1:49