SOLUTION: Hello, have a good day. I need quite some help here :( The problem is of the "Concepts review problems" type. It challenges the student to find out tricks or shortcuts to work out

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Question 939118: Hello, have a good day. I need quite some help here :(
The problem is of the "Concepts review problems" type. It challenges the student to find out tricks or shortcuts to work out problems without having specific numbers or values. I get always stuck here and I would like an explanation on how I should tackle the problem. How should I approach this type of questions:
"Let x and y be real numbers. If y > 1, compare: A. x+1/y+1 B. x/y +1"
Possible answers are: "A" if A is greater. "B" if B is greater. "C" if A is equal to B. "D" if we are not given enough information to work out an answer.
Thank you in advance.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
We are not given enough information. Only that y > 1. We are not given 
that x is not negative.  So here are three cases, one for A < B, one 
for A = B, and one for A > B.


 x   y         A=(x+1)/(y+1)                  B=(x/y)+1         A ? B
---------------------------------------------------------------------
 0   4    (0+1)/(4+1)=1/5=.2              0/4+1 = 0+1 = 1       A < B             
-4   2   (-4+1)/(2+1)=(-3)/3=-1      (-4)/(2)+1 = -2+1 =-1      A = B
-10  2   (-10+1)(2+1)=(-9)/3=-3       (-10)/2+1 = -4            A > B           

Incidentally if we had been given that x ≥ 0, then we could have 
concluded that A < B, but we can't since all we are given is that
x is a real number.

Edwin

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