Question 1076748
Find the range of values of x for: [(4-4x^2)/(X^2+1)^2]>0
If you look at the denominator, the denominator is always greater than zero because any nonzero number squared is a positive number.
We should focus on the numerator.  Look at (4 - 4x^2) > 0.  We get here because we can multiply both sides of the inequality by (x^2 + 1)^2, cancelling it out from both sides of the inequality.
Now solve for x in (4 - 4x^2) > 0
4 > 4x^2
1 > x^2
sqrt(1) > sqrt(x^2)
1 > |x|
We see that by the definition of absolute value we get
Either 1 > x OR 1 > -x
1 > x OR -1 < x
so  -1 < x < 1 is our solution.