SOLUTION: Determine Algebraically weather the function is even, odd, or neither. h(x)= x / (x^2-1) or x over x squared minus one My understanding>> I know you can fill

Question 180333This question is from textbook Algebra & Trigonometry
: Determine Algebraically weather the function is even, odd, or neither.
h(x)= x / (x^2-1) or x over x squared minus one
My understanding>> I know you can fill in h(-x) at which point if the answer comes out to be h(-x) then it is odd, or h(x)then it is even. If the answer is neither then it is (well) neither.
Where I get confused is >> When I fill in negative x to the denominator I then have a negative numerator and a negative denominator which in turn becomes positive (right?). Then, when my fraction becomes positive- do I change the (-1) to a (+1) [second position of the denominator]?
Afterwards, should I cross multiply (assuming the value of h(-x) can be placed over one.. OR should I multiply both sides by my denominator and work from there?
Please help.This question is from textbook Algebra & Trigonometry

Answer by stanbon(48558) (Show Source):
You can put this solution on YOUR website!
Determine Algebraically weather the function is even, odd, or neither.
h(x)= x / (x^2-1)
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h(-x) = (-x)/[(-x)^2-1] = -x/(x^2-1
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-(h(-x)) = x/(x^2-1)
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Since h(x) = -h(-x) the function is symmetric to the origin.
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Cheers,
Stan H.