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I can't get anywhere with this:

 

Find all x such that (x^2 - 4x + 5)/(9 - x^2) > 0.

 Aug 21, 2020
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Let us try integer values of x, if the problem means integers or else it is indefinite. If x=0, 0-0+5=5, and 9-0^2=9-0=9. Therefore 5/9>0. 
If x=1, 1-4+5=2, and 9-1=8 so 2/8>0.
x=2, 4-4+5=5, 9-4=5. 5/5>0.
x=3: 9-12+5=2, 9-9=0?!?!??!?! 2/0 is undefined. 3 is not a solution!!!
x=4. We already know this is negative.
x=5. This = 0.
x=6 Still negative, so greater than 6 is negative.
x=-1, positive.
x=-2, still positive.
x=-3, undefined.
x=-4, negative.
x=- anything greater than 4, NEGATIVE!!!
Therefore -4<=x<=2

 Aug 21, 2020

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