Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 123465: 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.
: 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.

Answer by jim_thompson5910(8292) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= unknown number


To find out what's going on, we have to translate this sentence into an algebraic expression:

First let's square the unknown number to get x^2

Now subtract 1 to get x^2-1

Divide the result by that number minus 1 (ie X-1) to get (x^2-1)/(x-1)


Now subtract the original number x to get (x^2-1)/(x-1)-x




So the sentence translates to (x^2-1)/(x-1)-x. Now let's simplify:



(x^2-1)/(x-1)-x Start with the given expression


(x+1)(x-1)/(x-1)-x Factor x^2-1 into (x+1)(x-1) by using the difference of squares



(x+1)cross((x-1))/cross((x-1))-x Cancel like terms


x+1-x Simplify


x-x+1 Group like terms


1 Combine like terms


So (x^2-1)/(x-1)-x simplifies to 1. In other words, (x^2-1)/(x-1)-x=1 for any x but x<>1. Can you see why?


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As for your own number game, you could try...

Take any number, square it, and add 6 multiplied by the original number. After that add 5. Now divide this by the original number plus one. Now subtract your original number to get 5.


This long sentence translates to ( tell me if you need help with the translation)

(x^2+6x+5)/(x+1)-x


(x+5)(x+1)/(x+1)-x Factor x^2+6x+5 to get (x+5)(x+1)


(x+5)cross((x+1))/cross((x+1))-x Cancel like terms


x+5-x Simplify


x-x+5 Group like terms


5 Combine like terms


So (x^2+6x+5)/(x+5)-x simplifies to 5. In other words, (x^2+6x+5)/(x+1)-x=5 for any x but x<>-1. Can you see why?