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Arithmetic and rational expressions

A rational expression, also known as a fraction, is really just the quotient of two integers. Let's look at how to add rational expressions. Adding rational expressions involves more or less the same rules as adding fractions. In order to add two fractions, we must find common denominators between the two. So also with rational expressions. We simplify both kinds of expressions the same way as well.

It is important to ensure that only common factors of the two rational expressions are cancelled rather than terms within the numerators and the denominators. For example, in attempting to simplify 2x + 6/x^2 + 6 we would not write 2x/x^2. To write this would be to commit the aforementioned error. 6 is not a common factor between the numerator and the denominator of the rational expression. It's just a term in the numerator and the denominator. We cancel common factors between the numerator and the denominator, not terms.

First, factor the denominator of both expressions. Next, multiply each rational expression by the denominator of the other one. Next, we add the numerators, but not the denominators, together, as is the case with ordinary addition of fractions. Finally, you have a simplified rational expression.