Module 3: Adding and Subtracting Rational Expressions
Section III: Rational Expressions, Equations, and Functions
[pic]
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. |
| |
|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:
[pic]
[pic]
[pic]
d. For this example it is helpful to recognize the following fact: –(a – b) = b – a
[pic]
[pic]
[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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