document.write( "Question 300230: Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. You reached 1 for an answer, didn’t you? How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it for your classmates to solve. Be sure to think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.
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Algebra.Com's Answer #215471 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Start with any number (but NOT 1)\r\n" );
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document.write( "Say \r\n" );
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document.write( "Square that number:\r\n" );
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document.write( "Subtract \r\n" );
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document.write( "Divide by one less than your original number.\r\n" );
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document.write( "The original number was .  One less than  is .\r\n" );
document.write( "So dividing  by \r\n" );
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document.write( "Now subtract your original number.\r\n" );
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document.write( "You reached .\r\n" );
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document.write( "That works for all numbers. Why does it work?  \r\n" );
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document.write( "Start with any number\r\n" );
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document.write( "Say \r\n" );
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document.write( "Square that number:\r\n" );
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document.write( "Subtract \r\n" );
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document.write( " \r\n" );
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document.write( "Divide by one less than your original number.\r\n" );
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document.write( "The original number was .  One less than  is .\r\n" );
document.write( "So dividing  by \r\n" );
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document.write( "Now subtract your original number, which was \r\n" );
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document.write( "You reached .\r\n" );
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document.write( "Notice that you could not have started with 1 because you\r\n" );
document.write( "cannot divide by 1 less than 1 because that would be dividing\r\n" );
document.write( "by zero!\r\n" );
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document.write( "You can make up a rational expression with a factor in the bottom\r\n" );
document.write( "that will cancel a factor in the top.  Say you start with this\r\n" );
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document.write( "Then multiply the top out:\r\n" );
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document.write( "Then to make the numerator , you say\r\n" );
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document.write( "Start with any number (other than 2).\r\n" );
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document.write( "Square it (that gives \r\n" );
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document.write( "Add the original number (that gives \r\n" );
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document.write( "Subtract 6  (that gives \r\n" );
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document.write( "Divide by 2 less than the original number (that gives \r\n" );
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document.write( "Subtract your original number  (that gives \r\n" );
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document.write( "You reach 3.\r\n" );
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document.write( "Try it with an arbitrary number.\r\n" );
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document.write( "Start with any number (other than 2).  Say we start with 83\r\n" );
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document.write( "Square it (that gives \r\n" );
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document.write( "Add the original number (that gives \r\n" );
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document.write( "Subtract 6  (that gives \r\n" );
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document.write( "Divide by 2 less than the original number (2 less than 83 is 81.\r\n" );
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document.write( "Subtract your original number  \r\n" );
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document.write( "You reach 3.\r\n" );
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document.write( "You cannot start with the number 3 because you would have to\r\n" );
document.write( "divide by 0.\r\n" );
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document.write( "Edwin

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