How Rational Expressions are like Fractions

Let's talk about rational expressions. When it comes to rational expressions, you need to know two things: factoring polynomials and fractions. It is important to know fractions because the steps for doing an operation with rational expressions is similar to an operation done between two fractions. Factoring is important because you can only cancel out factors with factors just like fractions.

In this post, I will compare the operations with fractions with rational expressions. I will line them up side by side. They should be the same if you set x equal to zero.

1. Simplifying rational expressions is like simplifying fractions

Note: you can only cancel out factors with factors.

2. Multiplying rational expressions is like multiplying fractions


Note: you can cancel within the same fraction or diagonally. It is always a factor of a numerator with the same factor in the denominator.

3. Dividing rational expressions is like dividing fractions





















Note: you have to first k-c-f it before you cancel things out. K-C-F stands for keep it, change it, and flip it.

4. Adding and subtracting rational expressions is like adding and subtracting fractions

Note: When you are adding and subtracting fractions, you have to find the LCD and equivalent fractions first to add the numerators. The denominators have to be the same. You don't cancel anything till its one fraction.

Simplifying rational expressions can be difficult, but remember they are just like fractions.