Log In

My Passes

Sign Up
Learning Guides
Teacher Resources
Test Prep
College Readiness
Schools & Districts
All of Shmoop
Literature
Bible
Poetry
Shakespeare
Mythology
Bestsellers
Dr. Seuss
PreAlgebra
Algebra
Algebra II
Geometry
Biology
US History
Flashcards
DMV
Careers
SAT
ACT
AP Exams
En Español
Essay Lab
Videos
Literary Critics
Shmoop Shtuff
Cite This Page
To Go
Rational Functions
Home
Algebra II
Rational Functions
Exercises
Intro
Topics
Examples
Exercises
Terms
Best of the Web
Quizzes
Handouts
Table of Contents
Advertisement
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 kneedeep 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 evershrinking 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 fancyshmancy: 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...
Need help with College?