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Simplifying Rational Expressions

Simplifying Rational Expressions

Author: chris ludbrook

1.  Simplify rational expressions.

2.  Multipliy and divide rational expressions.

3.  Find domain of simplified expressions, if necessary.

4.  Find LCM and LCD.

5.  Add and subtract rational expressions.


We have spent a lot of time working with polynomial expressions and equations.  In this unit, we will examine new equations that are formed by writing a ratio of two polynomial expressions.  Before we can examine the behavior of these equations both algebraically and graphically, we need to do some review of operations with polynomial expressions.  In this section we will work with multiplying and dividing polynomial expressions which requires much review of the factoring we have used before. 

Remember, a ratio of two polynomial expressions is called a rational expression.  In general, a rational expression is considered to be in simplified form if the numerator and denominator have no common factors other than 1.

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Introduction to Simplifying Rational Expressions

Here is a fairly clear and quick explanation of simplifying rational expressions as well as a discussion about domain.

Simplifying Rational Expressions with Quadratics

An example problem that involves the factoring of a polynomial. And a different explanation of some rules for simplifying.

Source: jcmaslan

Simplifying Rational Expressions with More Complex Quadratics

A slightly more challenging example of rational expressions with two quadratics. More importantly, there's a great discussion of how to factor quadratics by grouping.

Source: Khan Academy

Intro Vocab--Adding and Subtracting Rational Expressions

Finding LCM and LCD

A discussion on finding least common multiples with several examples.

Solving Rational Equations

Several examples (from easy to slightly more complex) of solving rational equations.

Source: Khan Academy

Laws of Exponents

This a great reference sheet for this unit as well as many others.