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# Rational Functions

# Rational Functions Examples

#### Simplifying Rational Expressions

If your first reaction is to run screaming from your computer whenever numbers get too complicated (like, fancier than "1 + 1"), calm down and think "simple." Wrestle down those big, bad r...

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

#### Complex Rational Expressions

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. There's one caveat: these expression...

#### 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. Once we figure out how to calculate the solut...

#### 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 it...

#### Solving Rational Equations

But wait, there's more. Solutions. How do we solve these bad boys? Here's how. Remember, a rational equation is an equation with at least one rational expression. To solve a rational equation, we m...

#### 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. It can be summed up as what goes up goes down and what does down goes up. This numerical seesawing goes on and on till you...

#### Joint Variation

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

#### 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 fo...

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