Algebra 2 Help? please i need help!

Question

1)Create a rational expression to be your game piece. You may choose from the list of factors below or make your own. There must be a variable term in both the numerator and denominator.
(5x)
(2x)
(x + 4)
(x – 5)
(2x + 1)
(3x + 5)
2)Turn one. Flip your coin and perform the appropriate operation. Explain to the game master how to add your rational expression to the one on the correct space. Use complete sentences.
3)Turn two. Flip your coin and perform the appropriate operation. Discuss and identify any possible restrictions that exist with (or in) the resulting rational expression.
4)Turn three. Flip your coin and perform the appropriate operation. Explain to the game master how to multiply your rational expression to the one on the correct space. Use complete sentences.
5)Turn four. Flip your coin and perform the appropriate operation. Discuss why the degree of the resulting denominator did not change from your expression’s degree.
6)Turn five, the final level! Perform the appropriate operation. Using complete sentences, describe the steps you used.

Answer 1

It looks like we are missing some of the information, but I think I understand and I will do my best.

 

Step 1
We need to pick an expression that we will be using for the next five steps. This should be something you are comfortable operating with. For the sake of example, I will pick one that involves both a coefficient to the variable and a constant to add to it. (3x + 5)

 

Step 2

I assume that the coin flip is what designates the other expression you will be working with. Let's say that you get (2x + 3). For this step we will be adding the expressions together.
(3x + 5) + (2x + 3) = 5x + 8. You would explain that the variables get added together (3x + 2x = 5x), and that the constants get added together (5 + 3 = 8). The expression cannot be simplified any more than that, so the final answer is 5x + 8

 

Step 3

Judging from the context of the instructions, it looks like you will be dividing your expression by another one. Let's say our coin landed on the expression (2x).
(3x + 5)/(2x) is the new expression. The restriction in this case is that x cannot be equal to 0, because dividing by 0 is impossible. Any other value for x would be acceptable.

 

Step 4
For this one we are going to multiply. If we land on (x - 6) then we will come up with this
(3x + 5)*(x - 6). Remember to FOIL. Multiply the first terms in each expression (3x * x = 3x²), then multiply the two terms on the outside (3x * -6 = -18x), then the two on the inside (5 * x = 5x), and then the multiply the last term of each expression together (5 * -6 = -30). Finally, we are going to add all of these together (3x² +5x - 18x - 30 = 3x² - 13x -30)

 

Step 5

For this one I am not sure what operation is being used, but the answer to the question is the same regardless. If you are inverting your expression (raising it to the power of -1 so that it becomes 1/(3x + 5)

 You're just flipping it upside down) then the degree (whether you have x or x²) is the same because the operation does nothing to affect the degree of the expression.

Contrast this with Step 4, where multiplying did change the degree from first power (x) to second power (x²)

 

Step 6
This last step is just a review of everything we have already done. Use the same processes as I have shown you, and you'll be fine.

I hope that helps
~Bruce