# Rational Functions Examples

#### Simplifying Rational Expressions

A rational expression is just a ratio (fraction) of two polynomials, kinda like a rational number is a ratio of two integers. The word "rational" has "ratio" tucked right in there, so it's easy...

#### Adding and Subtracting Rational Expressions

Remember fractions? They're about to rear their ugly heads again in the world of rational expressions. Rational expressions behave just like fractions, except they're more ornery. (It's those extra...

#### Multiplying and Dividing Rational Expressions

We multiply and divide rational expressions just like fractions. Wait—is this thing on repeat? To multiply rational expressions, first factor all numerators and denominators and cancel any factor...

#### Complex Rational Expressions

You thought you were knee-deep in complexity up to now? Brace yourself. Welcome to the wacky world of complex rational expressions. These guys have fractions inside their fractions. They may driv...

#### Evaluating Rational Functions

It doesn't take a lot of heavy mathematical lifting to work through rational functions. We just plug in numbers. That's it—at this stage of the game, anyway. Once we figure out how to calculate...

#### Graphing Rational Functions

Don't worry if the last time you graphed something was when you were tracking the life and hard times of your ever-shrinking bank account. Graphing rational functions is not rocket science, and i...

#### How to Solve Rational Equations

But wait, there's more. Solutions. How do we solve these bad boys?A rational equation is an equation with at least one rational expression all up in it. That means fractions. To solve a rational eq...

#### Direct Variation

As the song sort of goes, what goes up goes up, and what goes down goes down.The general form for direct variation looks like this:
y = kx This states that y varies directly with x, where k is a co...

#### Inverse Variation

If you thought direct variation was a cinch, welcome to inverse variation. When two variables vary inversely, that means what goes up goes down, and what does down goes up. This numerical seesawing...

#### Joint Variation

Now, let's deal with joint variation, where one is never enough. In fact, one seriously depends on two others, making a mathematical trio. Turns out it's not so fancy-shmancy: joint variation is...

#### Combined Variation

Last, but in no way least, is combined variation. Numbers are mixed, matched, computed, jumbled, and ultimately combined.
Combined variation mixes both direct and inverse variation. The general...