已知x:y=-2:3,求(x^2-y^2/xy)^2/[(x+y)*[(x-y)/x]^3/(x/y^2)的值
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∵x:y=-2:3
∴x=-2y/3
(x^2-y^2/xy)^2/[(x+y)]*[(x-y)/x]^3/(x/y^2)
=[(x-y)(x+y)/xy]²/[(x+y)(x-y)³/x³]/(x/y²)
=(x-y)²(x+y)²/x²y²*[x³/(x-y)³(x+y)]*(y²/x)
=(x-y)²(x+y)²(x³y²)/[(x²y²)*(x-y)³(x+y)*x]
=(x+y)/(x-y)
=(-2y/3+y)/(-2y/3-y)
=(y/3)/(-5y/3)
=-1/5
∴x=-2y/3
(x^2-y^2/xy)^2/[(x+y)]*[(x-y)/x]^3/(x/y^2)
=[(x-y)(x+y)/xy]²/[(x+y)(x-y)³/x³]/(x/y²)
=(x-y)²(x+y)²/x²y²*[x³/(x-y)³(x+y)]*(y²/x)
=(x-y)²(x+y)²(x³y²)/[(x²y²)*(x-y)³(x+y)*x]
=(x+y)/(x-y)
=(-2y/3+y)/(-2y/3-y)
=(y/3)/(-5y/3)
=-1/5
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