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.
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
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:
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