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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.

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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...

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...and makes the guys solve math problems to figure out what

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their "special number" will be for the rest of the year.

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Sam gets an anonymous letter under his door that says,

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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,

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3 goes into 36 twelve times and 3 goes into 3 one time...

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...so 36 minus 3p becomes 3 times 12 minus p.

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We can see that in the denominator the greatest common factor is 4.

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4 goes into 4 one time and goes into 48 twelve times...

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...so we can factor out the 4 to get 4 times p minus 12.

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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 1 from the top...

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to get negative 3 times p minus 12, over 4 times p minus 12.

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The top and bottom of the expression have common factors of p minus 12,

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so we can just 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!

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He has so got this college thing in the bag.

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