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. Did you reach 1 for an answer? You should have. 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?

ex) 5

5^2= 25-1= 24/4= 6-5= 1
yes
It works because if you work backwards you get your original number.

Evaluate 5(11 + 22 - 10) – 19

The number game you described can be better understood by following these steps with a variable instead of an actual number:

1. Take any number (let's call it x).
2. Square that number, which would be x^2.
3. Subtract 1 from the squared number: x^2 - 1.
4. Divide by one less than your original number, which is (x - 1).
5. Now, subtract your original number (x).

So, the rational expression for this number game would be:

((x^2 - 1) / (x - 1)) - x.

To understand how this number game works, let's simplify the rational expression:

((x^2 - 1) / (x - 1)) - x.

To simplify this expression, we need to find a common denominator. The denominator (x - 1) can be multiplied by (x + 1) to make it the common denominator:

((x^2 - 1) - x(x + 1)) / (x - 1).

Now, simplify further:

(x^2 - 1 - x^2 - x) / (x - 1).

Combine like terms in the numerator:

(-1 - x) / (x - 1).

Finally, simplify:

-(x + 1) / (x - 1).

As you can see, the simplified rational expression is -(x + 1) / (x - 1). Regardless of the value of x (as long as it is not 1), the numerator will always be -(x + 1). So, the result will be -1, which is why you reached 1 in your original number game.

By simplifying rational expressions, we can analyze their behavior and determine if there are any factors or common terms that can be canceled out. In the case of this number game, simplifying the rational expression showed that the numerator is always -(x + 1), indicating that the outcome will always be -1.