SOLUTION: 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 posit

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.
Found 2 solutions by alanc, rapture:
Answer by alanc(27) (Show Source): You can put this solution on YOUR website!
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.
Answer by rapture(86) (Show Source): You can put this solution on YOUR website!
You want the fraction to be greater than zero.
A fraction is positive either when both numerator and denominator are positive or when both are negative. In this case the denominator is positive for each x. So, you have to find for which values of x the numerator is also positive.
I hope this helps.

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