Take any number other than 1. Square that number and then subtract 1. divide by one less than your original number. now subtract your original number. you should end up at one. how does this work?? Rewrite and use a variable instead of and actual number and rewrite the problem as one rational expression.

let your number be x

square that number --- x^2
subtract 1 ----- x^2 - 1
divide by one less than original number ---- (x^2 - 1)/(x-1)
= (x+1)(x-1)/(x-1)
= x+1
subtract original number
x+1 - x
= 1

To understand how this mathematical statement works, let's rewrite it using a variable to represent the number:

Let's assume our original number is represented by "x".

According to the given statement, we need to follow the following steps:

Step 1: Square the number and subtract 1.
- (x^2) - 1

Step 2: Divide the result from step 1 by one less than the original number.
- ((x^2) - 1) / (x - 1)

Step 3: Finally, subtract the original number.
- ((x^2) - 1) / (x - 1) - x

If we simplify the expression in step 3, we get:
- ((x^2) - 1 - x(x - 1)) / (x - 1)
- (x^2 - 1 - x^2 + x) / (x - 1)

Now, let's simplify further:
- (-1 + x) / (x - 1)
- (x - 1) / (x - 1)

When we simplify this expression, we obtain:
1

Therefore, regardless of the value of "x" (as long as it is not equal to 1), the result of this expression is always 1.