SOLUTION: Evalute the expression when x=-1, x=0, and x=1. Then determine whether the result is a whole number, an integer, or a rational number. x2+1 _____ x-3

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Question 103035: Evalute the expression when x=-1, x=0, and x=1. Then determine whether the result is a whole number, an integer, or a rational number.
x2+1
_____
x-3

Found 2 solutions by elima, Fombitz:
Answer by elima(1433) About Me  (Show Source):
You can put this solution on YOUR website!
Evalute the expression when x=-1, x=0, and x=1. Then determine whether the result is a whole number, an integer, or a rational number.
x2+1
_____
x-3
1)x=-1
%28%28-1%292%2B1%29%2F%28-1-3%29
%28-2%2B1%29%2F-4
1%2F4
rational
2)x=0
%28%280%292%2B1%29%2F%280-3%29
1%2F-3
rational
3)x=1
%28%281%292%2B1%29%2F%281-3%29
3%2F-2
rational
:)

Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
Let's get some definitions first.
Whole numbers : 0,1,2,3,4,...
Integers : Whole numbers and negative whole numbers : ...,-4,-3,-2,-1,0,1,2,3,4,...
Rational numbers : Numbers defined as ratios of integers : 1/2, 5/6, 8/3,...
f%28x%29=%28x%5E2%2B1%29%2F%28x-3%29
When x=-1
f%28-1%29=%28%28-1%29%5E2%2B1%29%2F%28-1-3%29
f%28-1%29=%282%29%2F%28-4%29
f%28-1%29=+1%2F2
1/2 is a rational number
f%28x%29=%28x%5E2%2B1%29%2F%28x-3%29
When x=0
f%280%29=%28%280%29%5E2%2B1%29%2F%280-3%29
f%280%29=%281%29%2F%28-3%29
f%280%29=+-1%2F3
-1/3 is a rational number
f%28x%29=%28x%5E2%2B1%29%2F%28x-3%29
When x=1
f%281%29=%28%281%29%5E2%2B1%29%2F%281-3%29
f%281%29=%282%29%2F%28-2%29
f%281%29=+1
1 is a rational number (1/1), an integer, and a whole number