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Polynomial Division and Rational Expressions

Polynomial Division and Rational Expressions


After looking for single-term common factors, the next thing to do is to factor the numerator and denominator to see if there are any other factors we can cancel. We're on an absolute canceling tear. We can't be stopped!

Okay, fine. If it looks like factoring the numerator and factoring the denominator are reasonable tasks, go for it. Otherwise, skip this step. We're on an absolute unreasonable step-skipping tear. We can't be stopped!

Sample Problems

Simplify the rational expression as much as possible.

First off, our expression factors as . We can cancel out a factor of (x + 1) from the numerator and denominator, which leaves us with .

Meanwhile, the expression is way too grody to factor. Our eyes are burning from looking at it. However, it turns out to factor quite nicely:

But there's no way to know this from looking at it unless you're some kind of mathematical savant. If you are, what in the world are you doing here? Don't you have bigger fish to fry?

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