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Chapter 0: Problem 102

Explain how to add or subtract rational expressions with the same denominators.

Short Answer

Expert verified
To add or subtract rational expressions with the same denominators, combine the numerators by addition or subtraction, and place the result over the common denominator. Simplify if necessary.

Step by step solution

01

Identify the Denominators

Check that the rational expressions have the same denominator. If they do not, they will need to be made the same before they can be added or subtracted. In this case, the problem states that the denominators already match, so this step is complete.
02

Combine the Numerators

Combine the numerators of each rational expression by adding or subtracting as the problem instructs. Write the result over the common denominator. For example, if the expressions are \(\frac{a}{c}\) and \(\frac{b}{c}\), and you are asked to add them, combine the numerators to get \(\frac{a+b}{c}\). If you are subtracting, the result would be \(\frac{a-b}{c}\).
03

Simplify the Resulting Expression

If possible, simplify the resulting expression. Look for common factors in the numerator and denominator, and divide by the common factors to simplify.

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