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Adding Rational Expressions

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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 these lessons, we will learn how to add rational expressions with the same denominator and how to add 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.


Simplify the following rational expression


Add Rational Expressions

How to add rational expressions that have a common denominator, and how to simplify if it is possible to cancel? 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.

Step 3: Add the numerators and simplify when possible.

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


Express the following as fractions with a single denominator:


Simplify Rational Expressions

Add and Subtract Rational Expressions - Unlike Denominators
How to add and subtract rational expressions when the denominators are different? How to add rational expressions with different denominators? How to add rational expressions with different monomial denominators?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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