I can't get anywhere with this:

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

Guest Aug 21, 2020

#1**0 **

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

Pangolin14 Aug 21, 2020