化简求值:(1)已知x+y=6,xy=-2,求(x^4-y^4)÷(x^2+y^2/xy)÷(6x-6y);

题目

化简求值:(1)已知x+y=6,xy=-2,求(x^4-y^4)÷(x^2+y^2/xy)÷(6x-6y);
PS:"/"为分数线.

答案

(x^4-y^4)÷(x^2+y^2/xy)÷(6x-6y)
=(x²+y²)(x+y)(x-y)×[xy/(x²+y²)]×1/6(x-y)
=xy(x+y)/6
=-2×6/6
=-2