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Solving Rational Equations with One Variable, a la Shmoop

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The brother of a handsome, but rather dopey, gold-medal swimmer also has a reality show.

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His name is Bryan and he is a mathematician.

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Bryan is trying to figure out how many viewers he can expect for his show.

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The network execs have given him a formula to figure out how many viewers Brian can expect.

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Seven over two v, plus one over four, equals seventeen over four v.

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Solving for v will tell us the number of viewers.

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How many viewers will be tuning in to Brian's show?

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Not counting yourself, of course.

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Here are your options.

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First, Brian has to find the lowest common multiple, or LCM, of the denominator.

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This is only slightly more difficult than counting his brother's brain cells.

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The lowest common multiple is 4v.

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To get 4v in the denominator, we have to multiply 2v by 2.

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And whatever you do to the bottom, you have to do to the top.

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So we can multiplying seven over 2v by two over two to get fourteen over 4v.

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To get 4v on the bottom of this fraction, multiply one over four

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by v over v, which is one, giving us v over 4v.

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Seventeen over four-v is fine. We don't need to change it.

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Since every term in the equation is over 4v,

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we can just multiply the equation by 4v to get rid of it.

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Now we're left with fourteen plus v equals seventeen.

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Subtract 14 from both sides to isolate v...

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v equals seventeen minus fourteen, which is three.

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So the answer is A. Three.

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Sorry Bryan.

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I guess only you and your cats watch your show.

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