已知:{x^2-y^2=16,x+y=2;求(3x-3y)/(y^2-x^2)+(x^2-2xy+y^2)/(x^2-y^2)-(x^2-x-6)/(x+2)÷(x+y)的值
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x+y=2 (1)
x^2-y^2=(x+y)(x-y)=16
所以 x-y=16/2， x-y=8 (2)
由（1）（2）解得 x=5，y= -3
(3x-3y)/(y^2-x^2)+(x^2-2xy+y^2)/(x^2-y^2)-(x^2-x-6)/(x+2)÷(x+y)
=3(x-y)/(y+x)(y-x)+(x-y)^2/(x+y)(x-y)-(x+2)(x-3)/(x+2)÷(x+y)
= -3/(x+y)+(x-y)/(x+y)-(x-3)÷(x+y)
=[-3+(x-y)-(x-3)]/(x+y)
= -y/(x+y)
= -(-3)/2
=3/2
x^2-y^2=(x+y)(x-y)=16
所以 x-y=16/2， x-y=8 (2)
由（1）（2）解得 x=5，y= -3
(3x-3y)/(y^2-x^2)+(x^2-2xy+y^2)/(x^2-y^2)-(x^2-x-6)/(x+2)÷(x+y)
=3(x-y)/(y+x)(y-x)+(x-y)^2/(x+y)(x-y)-(x+2)(x-3)/(x+2)÷(x+y)
= -3/(x+y)+(x-y)/(x+y)-(x-3)÷(x+y)
=[-3+(x-y)-(x-3)]/(x+y)
= -y/(x+y)
= -(-3)/2
=3/2
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