Reducing fraction with quadratic in the numerator

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maroonblazer
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Reducing fraction with quadratic in the numerator

Postby maroonblazer » Sat Sep 18, 2010 7:59 pm

Hi,
The book I'm working through asks the following:
When reduced to lowest terms, a fraction whose numerator is x^2 - 3x + 2 equals -1. What is the denominator of the fraction? Explain your answer.


I can factor the numerator to (x-2) (x-1), but I'm struggling to determine what denominator would leave -1 when simplified.

Ideas?

Thanks in advance,
mb

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stapel_eliz
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Postby stapel_eliz » Sun Sep 19, 2010 1:23 am

When reduced to lowest terms, a fraction whose numerator is x^2 - 3x + 2 equals -1. What is the denominator of the fraction? Explain your answer.

What is the value of (-5)/5? What is the value of 7/(-7)? What is the value of (3.5)/(-3.5)?

With that in mind, note that x - a = -a + x = -(a - x). (An example is shown here. Scroll down to the second example.)

Can you figure out how to construct the factors in the denonimator to get the result you need? :wink:

maroonblazer
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Re:

Postby maroonblazer » Sun Sep 19, 2010 2:24 am

stapel_eliz wrote:
When reduced to lowest terms, a fraction whose numerator is x^2 - 3x + 2 equals -1. What is the denominator of the fraction? Explain your answer.

What is the value of (-5)/5? What is the value of 7/(-7)? What is the value of (3.5)/(-3.5)?

With that in mind, note that x - a = -a + x = -(a - x). (An example is shown here. Scroll down to the second example.)

Can you figure out how to construct the factors in the denonimator to get the result you need? :wink:


So is it as simple as making the denominator: (1-x)(2-x)?

mb

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stapel_eliz
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Postby stapel_eliz » Sun Sep 19, 2010 11:53 am

If both factors have their terms reversed, this will generate two "minus" signs, which, when multiplied, will cancel out. So how many of the denominator's factors should you reverse? (Note: There are two "right" answers to this exercise!) :wink:

maroonblazer
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Re:

Postby maroonblazer » Sun Sep 19, 2010 12:10 pm

stapel_eliz wrote:If both factors have their terms reversed, this will generate two "minus" signs, which, when multiplied, will cancel out. So how many of the denominator's factors should you reverse? (Note: There are two "right" answers to this exercise!) :wink:


Ah, got it. So possible answers are:
(1-x)(x-2)

or

(x-1)(2-x)

Thanks!


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