Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 33: Adding and Subtracting Rational Expressions
Answer/Discussion
to 1a
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The first denominator has the following factor: |
The second denominator, 5 - x, looks
like the first denominator except the signs are switched. We can
rewrite this as |
Putting all the different factors together and using the highest
exponent, we get the following LCD: |
Note that I did not put the -1 that was in front of the second denominator's
(x - 5) factor. In the step 3, I will put the negative into the problem
by placing it in the numerator of that second fraction. |
Now the two fractions have a common denominator, so we do not have
to rewrite the rational expressions. |
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*Combine the two num.
*Write over the common den.
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*Divide out the common factor of (x -
5) |
Answer/Discussion
to 1b

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The first denominator has the following factors: |
The second denominator has the following factor: |
Putting all the different factors together and using the highest
exponent, we get the following LCD: |
Since the first rational expression already has the LCD, then
we do not need to change this fraction. |
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*Rewriting denominator in factored form
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Rewriting the second expression with the LCD: |
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*Missing the factor of (a -
2) in the den.
*Mult. top and bottom by (a - 2)
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*Combine the two num.
*Write over the common den.
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*Divide out the common factor of (a - 3) |
Answer/Discussion
to 1c

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The first denominator has the following factor: |
The second denominator has the following factors: |
The third denominator has the following factors: |
Putting all the different factors together and using the highest
exponent, we get the following LCD: |
Rewriting the first expression with the LCD: |
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*Missing the factors 2 and x in the den.
*Mult. top and bottom by 2x
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Rewriting the second expression with the LCD: |
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*Missing the factor of x in the den.
*Mult. top and bottom by x
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Rewriting the third expression with the LCD: |
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*Missing the factor of 2 in the den.
*Mult. top and bottom by 2
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*Combine the three num.
*Write over the common den.
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*Divide out the common factor of (x + 2)
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Last revised on July 17, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward.
All rights reserved.
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