Adding Rational Expressions

A rational expression is a fraction in which either the numerator, or the denominator, or both the numerator and the denominator are algebraic expressions. For example, and are rational expressions.

In this lesson, we will be looking at how to add rational expressions with the same denominator and rational expressions with different denominators.

Adding Rational Expressions with Same Denominators

When the denominators of two algebraic fractions are the same, we can add the numerators and then simplify when possible.

Example:

Simplify the following rational expression

Solution:

The following video shows how to add or subtract rational expressions with same denominators.

Adding Rational Expressions with Different Denominators

When the denominators of two algebraic fractions are different, we need to find the LCM of the denominators (also called the LCD) before we add or subtract the fractions.

Here are the steps you need to follow:

Step 1: Find the LCD

Step 2: Express each fraction with the LCD as the denominator.

Now we apply the above 3 steps in the following examples.

Example:

Express the following as fractions with a single denominator:

Solution:

The following videos show how to add rational expressions with different denominators.

The following video shows how to add rational expressions with different monomial denominator.

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