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Multiplying Rational Expressions, a la Shmoop.

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In the distant future, arguments between friends and roommates will be solved with math.

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Today, we'll see how it might be used to solve a problem between two roommates on a space

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station orbiting Jupiter.

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Meet Xavier and Yumi.

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Their dilemma is represented by the following...

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4 x over 5 y squared times 20 x-squared y over y to the fourth.

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Now let's talk about what they have in common.

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Remember, usually when we multiply fractions, we multiply across top and bottom.

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But when we see a chance, we can simplify first by canceling any duplicate factors.

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Looking at our problem, we can see that the 20 in the top of the second fraction

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and the 5 in the bottom of the first fraction are both factors of 5.

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We can simplify by dividing 20 by 5 to get 4,

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and divide the 5 on the bottom by 5 to get 1.

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Looking at the second fraction, we can cancel the top y with the y to the fourth on the bottom...

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leaving y to the power of three.

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Now we can just multiply across the top of the two fractions...

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4 x times 4 x-squared equals 16 x-cubed.

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And multiply across the bottom... y-squared times y-cubed...

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...remember that we multiply two terms with the same base, and we can add the two exponents...

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in this case, the 2 and 3, to get y to the fifth.

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So the answer is 16 x cubed over y to the power of 5.

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And on the space station orbiting Jupiter, this result means that it's Xavier's turn

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to take out the plutonium.

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Don't forget to shut the airlock.

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