Expert: Richard J. Raridon - 9/27/2010

Question
QUESTION: 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.



ANSWER: You can see how it works by writing it in terms of x.  
If the number is x, then (x^2-1)/(x-1) = x+1 so when you subtract x, you get 1.

---------- FOLLOW-UP ----------

QUESTION: Thank you! So, how would I redo the number game using a variable instead of an actual number or is that what the "x" is for in the answer you gave.
I am really confused in Algebra, so I apologize if I am asking the same things more than once.
Also, how would I go about creating my own number game using the rules of algebra to post for my classmates to solve, thinking about values that may not work as well?
Also, another question in it, was "how did the number game use the skill of simplifying rational expressions?"

Answer
The "x" is the variable.  That just shows it works for any number. To follow the solution you needed to know that (x^2-1)/(x-1) = x+1.  
Here's another.  Tell someone to pick a 1 or 2 digit number.  Double the number.  Add 12.  Divide the total by 2.  Subtract the original number.  Ask them if they got 6.