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

All you have to do is create a number game. It shouldn't be too difficult. Just make sure you "undo" what you "do". If you add five, make sure you subtract five later on (maybe just not all at once so it doesn't look as obvious). Try to create one and check it and post it if you want.

The number game you are describing can be explained using algebraic expressions. Let's say your original number is represented by the variable "x".

Step 1: Square the number (x^2).
Step 2: Subtract 1 from the squared number (x^2 - 1).
Step 3: Divide by one less than the original number (x^2 - 1) / (x-1).
Step 4: Subtract your original number (x^2 - 1) / (x-1) - x.

The goal of this number game is to show that, regardless of the value of x (except for 1), the final result will always be 1. We can simplify the expression to demonstrate this.

To simplify the rational expression (x^2 - 1) / (x-1) - x, we can first find a common denominator by multiplying (x-1) with (x+1) on both numerator and denominator.

[(x^2 - 1) - x(x-1)] / (x-1)(x+1) simplifies to (x^2 - 1 - x^2 + x) / (x^2 - 1).

Next, we can combine like terms in the numerator:

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

Finally, we can further simplify the expression by factoring the denominator:

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

As we can see, no matter what value of x we use (except for x = 1), the numerator (-1 + x) will always cancel out with one of the factors in the denominator (x - 1 or x + 1), resulting in a simplified expression of 1.

This number game demonstrates the skill of simplifying rational expressions, as we have simplified the expression and shown that the final result is always 1.

Now, let's create a new number game using algebraic rules:

Number Game: Find the value of x that satisfies the following expression:

(x^2 - 4x - 5) / (x - 5) = 2.

To solve this number game, we can start by multiplying both sides of the equation by (x - 5) to eliminate the denominator:

x^2 - 4x - 5 = 2(x - 5).

Next, we can expand and simplify:

x^2 - 4x - 5 = 2x - 10.

Moving all terms to the left side:

x^2 - 4x - 5 - 2x + 10 = 0.

Combining like terms:

x^2 - 6x + 5 = 0.

Now, we need to factor this quadratic equation:

(x - 5)(x - 1) = 0.

From the factorization, we have two possible values for x: x = 5 or x = 1.

However, we need to consider the original equation (x^2 - 4x - 5) / (x - 5) = 2. If we substitute x = 5 into the equation, we will have a denominator of 0, which is not allowed. Therefore, the only valid solution for this number game is x = 1.

This number game also utilizes the skill of simplifying rational expressions and solving quadratic equations.