SOLUTION: Take any number (except for 1). 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 answ

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Question 221921: Take any number (except for 1). 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.

Consider responding to your classmates by solving their number game or expanding on their game to create an even more challenging one. You may want to review responses to your number game in case you need to make changes or help another student.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the chosen number.

Square the number:

Subtract 1:

Divide by one less than the original number:

Before we continue, simplify:

Subtract the original number:

Works for all . (Extra credit: why can't x = 1?)

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New Number Game: Prove that 2 equals 1.

Let

Multiply both sides by

Subtract from both sides:

Factor both sides:

Divide both sides by

But , so substitute:

Divide both sides by

The game is "What's wrong with this proof? What did I do wrong that allowed me to achieve a result that is obviously absurd?"

John