Symmetry? even or odd function?

Question

f(x) = (x^3 - x)/(x^3 - 4x)

describe the symmetry of the graph

is f an even or odd function?

and i cant use a graphing calc so it has to be done algabraically or calculus-ly. however you put it. lol

thanks in advance

Answer 1

f(x) = (x^3 - x)/(x^3 - 4x) = (x^2-1)/(x^2 -4)

becuase numerator and denominator both are symetric about y axis the function is symeric around y axis

this can ve verifed by checking f(-x) = (x)

hence the function is even as well