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00:03

Simplifying Rational Expressions, a la Shmoop.

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Sam is beginning his college career, and has just joined the fraternity, Alpha Delta Nerda. [Sam waving in corridor]

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School policy says that no physical hazing is allowed…

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…so Alpha Delta Nerda does its own kind of hazing… [Group of people studying]

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…and makes the guys solve math problems to figure out what their “special number”

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will be for the rest of the year.

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Sam gets an anonymous letter under his door that says, [Letter appears underneath a door]

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Simplify 36 minus 3p all over 4p minus 48.

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To start, let’s take a look at the numerator to see if we can factor out anything.

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We see that 3 is the greatest common factor of 36 and 3p, so we can factor out a 3…

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to get 3 times 12 minus p.

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In the denominator, we see that the greatest common factor is 4, so we can factor out a [Finger points to the denominator]

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4 from 4p and 48 to get 4 times p minus 12 on the bottom.

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12 minus p is the same as p minus 12… when multiplied by a negative.

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So we can pull out a negative one from the top…to get negative 3 times p minus 12,

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over 4 times p minus 12.

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The top and bottom of the expression have common factors of p minus 12, so we can just [p minus 12 common factors highlighted]

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cancel these out.

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And we’re left with negative three-fourths!

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That’s it! Sam’s special number is negative three-fourths! [Sam crunching special numbers]

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He has so got this college thing in the bag.

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