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Polynomial Division and Rational Expressions
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Polynomial Division and Rational Expressions
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Polynomial Division and Rational Expressions Examples
Common Factors
The easiest case of polynomial division is when the divisor is a single term that happens to be a common factor of the dividend. You'll love when this happens. For the sake of the integer analogy,...
Factoring
Factoring isn't only for when the divisor is a single term. We can use factoring to divide one polynomial by another polynomial, as long as the polynomial in the denominator is a factor of the poly...
Long Division
After looking for singleterm factors and finishing all our factoring, the next thing we do to divide polynomials is use good oldfashioned long division. You know, oldfashioned like the donut: de...
Common Factors
The first thing to do when dividing polynomials is to look for and remove common factors. In terms of rational expressions, "looking for common factors" means that we're looking for those that go i...
Long Division
Once we've canceled all the factors we can, we write out the new numerator and denominator (the unfactored versions) and look at their degrees. If it's too many degrees, we'll stay inside and eat c...
A Clever Trick
First, you take the rubber ball in your left hand, then tap the back of that hand with the wand held in your right. Say a few magic words, and then...oh. This isn't amateur magician hour? Our bad.W...
Simplifying Rational Expressions
When we're given a rational expression, we can simplify it by doing the first two steps of polynomial division: we cancel any common factors, then factor the numerator and denominator and cancel an...
Multiplying and Dividing Rational Expressions
MultiplyingAs you'll recall from that time you became the grandmaster lord high poobah of all things fractions, multiplying fractions requires us to multiply the numerator by the numerator and the...
Adding and Subtracting Rational Expressions
...with the same denominator Adding or subtracting rational expressions with the same denominator is like adding or subtracting fractions with the same denominator. We add or subtract t...
Simplifying Complex Rational Expressions
A complex rational expression is a rational expression in which the numerator and/or the denominator are rational expressions. In other words, a complex rational expression is a nastylooking ratio...
Equations Involving Rational Expressions
Solving an equation that contains rational expressions is similar to solving any old equation that has fractions in it. In fact, if the variable only occurs in numerators, we are actually solving a...
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