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Simplify Rational Expressions Practice 5 - Visualizing Algebra

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    We can factor this numerator as the difference of two squares. We can write it
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    as 6 minus x times 6 plus x. For this denominator we want to find the factors of
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    negative 48 that sum to positive 2. These factors are negative 6 and positive 8.
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    When I look at my factors it doesn't seem as if anything can simplify out to
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    equal 1 but if i look at these two factors i can see that these are opposite
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    polynomials. The constant term 6 is positive while this one's negative and the x
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    term is negative here while this x term is positive. This means I'll have a
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    factor of negative 1. We can see this if we were to just switch the order of the
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    terms for these two, we'll have negative 6 plus x, then I can factor a negative
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    1 from this factor. I'll have negative 1 times positive 6 minus x. I change the
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    signs of both of these terms since i factored a negative 1 out. These factors of
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    6 minus X simplified to 1 but i still have a negative 1 out in front, just like
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    I thought here. Whenever you see opposite polynomial factors you can simplify
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    them to be negative 1. We don't need to show all this work. So we're left with
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    this expression. Now, I want to acknowledge there are a lot of different answers
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    here. This negative sign could have been distributed to either the numerator or
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    the denominator. If we distribute the negative 1 to the numerator, we could have
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    gotten this expression. Or switch the order of these terms and you got this
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    expression. These are all equal. If we distribute this negative one instead of
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    the denominator, we can wind up with any of these expressions. And in fact, all
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    of these are correct. In general, it's easiest to list the negative sign out in
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    front of a fraction and then write your rational expressions.
Title:
Simplify Rational Expressions Practice 5 - Visualizing Algebra
Video Language:
English
Team:
Udacity
Project:
MA006 - Visualizing Algebra
Duration:
01:42
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