Reducing fraction with quadratic in the numerator

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maroonblazer
Posts: 51
Joined: Thu Aug 12, 2010 11:16 am
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Reducing fraction with quadratic in the numerator

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?

mb

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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?

maroonblazer
Posts: 51
Joined: Thu Aug 12, 2010 11:16 am
Contact:

Re:

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

mb

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
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!)

maroonblazer
Posts: 51
Joined: Thu Aug 12, 2010 11:16 am
Contact:

Re:

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

or

(x-1)(2-x)

Thanks!