HELP! Maths(show the step,plz)

原題好像是
[1/(x^3) + 1/(y^3)] / (1/x + 1/y)

[1/(x^3) + 1/(y^3)] / (1/x + 1/y)
= [(x^3 + y^3)/(x^3)(y^3)] / [(x + y)/xy]
= [(x + y)(x^2 - xy + y^2)/(x^3)(y^3)][xy/(x + y)]
= (x^2 - xy + y^2)/(x^2)(y^2)
= 1/(y^2) - 1/xy + 1/(x^2) (E)

又 如果是 [1/(x^2) + 1/(y^2)] / (1/x + 1/y) 的話:
[1/(x^2) + 1/(y^2)] / (1/x + 1/y)
= [(x^2 + y^2)/(x^2)(y^2)] / [(x + y)/xy]
= {[(x + y)^2 - 2xy]/(x^2)(y^2)}[xy/(x + y)]
= [(x + y)^2 - 2xy]/[xy(x + y)]
= (x + y)/xy - 2/(x + y)
= 1/y + 1/x - 2/(x + y) … 所以題目應該有問題= =..

because it is multiple choice, it is no need to calculate. it needs to find right answer.

put x=y,
so it becomes 1/x.

from answer, A,B,C are wrong because it is all adding together with denominate x^2.

D is wrong as equal 0, E is wrong also.

So, there is something wrong in answer.

出錯題目, 題目應該係 :
(1 / x^3 + 1 / y^3)/(1 / x + 1 / y)
而答案是 E.