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Polynomial Division and Rational Expressions

Polynomial Division and Rational Expressions

At a Glance - Evaluating Rational Expressions


Evaluating a rational expression is exactly like evaluating any other expression. We substitute values for variables, do some arithmetic, and see what we find. It's usually much prettier than what we were previously dealing with, because we don't have all those ugly x's and y's hanging around by the end of it. However, with rational expressions, there's one thing to be careful of: we aren't allowed to put in values that make the denominator 0, because then we'd be dividing by 0 and the world would come crashing down.

Chicken Little thought things were bad when that acorn beaned him in the noggin. Watch out, Chicken Little. You'd better keep your eyes peeled for a whole other breed of ovoid.

Sample Problem

Evaluate the rational expression at each given value of x.

1. x = -3

All we've gotta do is plug in x = -3 and do some math.

Ah, beautiful.

2. x = 0

Second verse, same as the first. Replace all those x's with 0s to get:

Remember, it's fine if one of our variables equals 0, as long as the denominator doesn't. If we have nothing on the bottom, we'll have some real problems. We also won't be able to visit any public beaches.

3. x = 2

Psych! We aren't allowed to do this, because we'll have (2)2 – 4 = 0 in the denominator. See? We told you: no dividing by 0 allowed. When, oh when, will we learn?

Exercise 1

Evaluate the rational expression for x = 1, or explain why it's impossible.


Exercise 2

Evaluate the rational expression for x = 0, or explain why it's impossible.


Exercise 3

Evaluate the rational expression for x = 2, or explain why it's impossible.


Exercise 4

Evaluate the rational expression for x = -2, or explain why it's impossible.


Exercise 5

Evaluate the rational expression for x = -3, or explain why it's impossible.


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