Module 3: Adding and Subtracting Rational Expressions



Section III: Rational Expressions, Equations, and Functions

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Module 3: Adding and Subtracting Rational Expressions

Adding and subtracting rational expressions works the same way as adding and subtracting fractions.

[pic] example:

[pic]

|[pic] The key step in adding or subtracting fractions involves creating common denominators. This is also the key step in adding or |

|subtracting rational expressions. |

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|To add or subtract rational expressions with like denominators, add or subtract the numerators and keep the same denominator: |

| |

|[pic] AND [pic] |

It is often useful to factor denominators so that it is easier to create common denominators.

[pic] example: Perform the indicated operations; simplify your result completely.

a. [pic] b. [pic]

c. [pic] d. [pic]

SOLUTIONS:

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[pic]

[pic]

d. For this example it is helpful to recognize the following fact: –(a – b) = b – a

[pic]

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[pic] Try these yourself and check your answers.

Perform the indicated operations; simplify your result completely.

a. [pic] b. [pic]

SOLUTIONS:

[pic]

[pic]

[pic]

[pic] example: If [pic], find and simplify the expression [pic].

SOLUTION:

[pic]

[pic]

[pic] Try this one yourself and check your answer.

If [pic], find and simplify the expression [pic].

SOLUTION:

[pic]

[pic] example If [pic], find and simplify the expression [pic].

SOLUTION:

[pic]

[pic]

[pic] Try this one yourself and check your answer.

If [pic], find and simplify the expression [pic].

SOLUTION:

[pic]

[pic]

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