Rational Expressions: The Basics

A rational expression is a fraction with letters in it, like $\frac{3x + 12}{x + 4}$. Two rules run this whole topic.

First, the bottom can never be zero. Any value of $x$ that makes the denominator zero is undefined and gets thrown out. To find it, set the bottom equal to zero and solve.

Second, you may cancel factors, not terms. A factor is something being multiplied. A term is something being added. So factor the top, factor the bottom, then cancel anything that matches. For , the top factors into , the cancels, and the answer is .