Take any number (except for 1). Square that number and then subtract one. Divide

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.

Explanation / Answer

using variables....   our number is n

[(n 2-1)/ (n-1) ] - n = 1

add n to both sides

(n2-1) /(n-1) = 1 + n

multiply by (n-1)   (n2-1) = (1+n)(n-1)

use FOIL (n2-1) = n2 -1

Here we see that we can plug in any number and our equation works.

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