(a²-b²)/(ab)-(ab-b²)/(ab-a²)可化简为已知x²+5xy+y²=0,则(y)/(x)+(x)/(y)的值为

(a²-b²)/(ab)-(ab-b²)/(ab-a²)可化简为
已知x²+5xy+y²=0,则(y)/(x)+(x)/(y)的值为

(a²-b²)/(ab)-(ab-b²)/(ab-a²)
=(a²-b²)/ab+b(a-b)/a(a-b)
=(a²-b²)/ab+b/a
=(a²-b²+b²)/ab
=a/b
x²+5xy+y²=0
x²+y²=-5xy
∴(y)/(x)+(x)/(y)=(y²+x²)/xy=-5xy/xy=-5