Overview
On this page, we review rational expressions (i.e. quotients of two polynomials), how to identify when they’re defined, and how to simplfy them by factoring.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand that division by zero is not defined, so a rational expression can be undefined for particular values of its variables.
- Be able to find the domain of definition of a rational expression, the set of values where it is defined.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Simplify a rational expression by factoring the numerator and denominator, then cancelling common factors.
To prepare for class
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Watch the following video (by Tyler Wallace) which shows how to evaluate a rational expression for particular values of its variables:
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Watch the following video (by PatrickJMT) which shows how to find the domain of definition of a rational expression:
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Watch the following video (by Khan Academy) which gives more examples of finding the domain of definition of a rational expression:
After class
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Watch the following video (by PatrickJMT) which shows examples of factoring and simplifying rational expressions:
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Watch the following video (by Tyler Wallace) which shows examples of factoring and simplifying rational expressions:
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Watch the following video (by NancyPI) which shows more examples of factoring and simplifying rational expressions, as well as finding the domain (here referred to as the restrictions on x):