# Adding and Subtracting Rational Expressions

Learning Objectives:

# Understand to Add and Subtract Rational Expressions

Let’s take a look at how we add or subtract with like denominators before we discuss how to add or subtract with unlike denominators. As we can see here, if we want to add or subtract fractions with like denominators we simply add or subtract the numerators and then simplify if possible.  To add or subtract rational expressions with unlike denominators we must first re-write each expression using the least common denominator ( lcd ). So we have to have a common denominator to add or subtract rational expressions. The lcd must contain all of the different factors in the polynomials and each factor must be repeated the maximum number of times it occurs in any one of the polynomials. So here's how we're going to do this. We'll factor all the denominators and we'll use these factors to determine the lcd, and then we'll multiply the numerator and denominator of each fraction by any missing factors to form the lcd. Then we'll add the fractions and simplify.

Hook questions:

1. How do you find the sum or difference of rational expressions with different denominators?

2. What is the definition of rational algebraic expression?

3. How do you add fractions with variables?

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