Simplifying rational expressions
A fraction has polynomials on top and bottom. How do you simplify it and combine it with others, and which values of the variable are never allowed?
Where you are 3 inside
What this area is about
A rational expression is a fraction whose numerator and denominator are polynomials, with a denominator that is not the zero polynomial, such as \displaystyle \frac{x + 1}{x^2 - 4}. Its arithmetic is the arithmetic of number fractions, with one extra duty: any value that makes a denominator 0 is excluded, and it stays excluded after canceling.
How these fit together
Definition and first procedure. Simplifying a rational expression and where it is undefined defines excluded values, then factors and cancels common factors. The short form equals the original only where the original is defined: \displaystyle \frac{x^2 - 9}{x - 3} = x + 3 for x \ne 3.
Operations. Multiplying and dividing rational expressions factor, flip the divisor, cancel and multiply, keeping every value excluded along the way. Adding and subtracting rational expressions rename each fraction over a common denominator, then combine the numerators, and simplify complex fractions.
A path through it
Start with simplifying and excluded values, which the multiplying lesson refers back to. Then multiply and divide, then add and subtract.
Next: solving a rational equation and rational functions.