1) Factor and simplify:
f(x) = [10x (x^2 - x - 1) ] / [ 2x (x^4 - 1) ] =5 (x^2 - x - 1) / (x^4 - 1)
2) Calculate limits
A) limit of f(x) when x -> 0 = 5(-1)/(-1) = 5
=> y-axis is not an asymptote and A is TRUE.
B) Lim of f(x) when x -> +/- ∞ =
5 * (x^2 / x^4 - x / x^4 - 1/ x^4 ) / (x^4 / x^4 - 1 /x^4) = 0 / ∞ = 0
=> x-axis is an asymptote and B is TRUE
C) Lim of f(x) when x -> - 1 =
5 * (x^2 - x - 1) / (x^4 - 1) = 5 * (1 + 1 - 1) / (1 - 1) = 5 / 0 = ∞
=> x = - 1 is an asymptote and C. is FALSE.
Now you have the answer.
If you want you can verify that the last option is TRUE.
I also enclose a picture showing the asymptotes which may help you.
Answer: Option C. is the false one.
