化简下面代数式(x+y/x-y+4xy/y^2-x^2)/x^2-4y^2/x^2+3xy+2y^2并求出x,y满足2^2+3xy-5y^2=0时,代数式的值
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![化简下面代数式(x+y/x-y+4xy/y^2-x^2)/x^2-4y^2/x^2+3xy+2y^2并求出x,y满足2^2+3xy-5y^2=0时,代数式的值](/uploads/image/z/5919075-27-5.jpg?t=%E5%8C%96%E7%AE%80%E4%B8%8B%E9%9D%A2%E4%BB%A3%E6%95%B0%E5%BC%8F%EF%BC%88x%2By%2Fx-y%2B4xy%2Fy%5E2-x%5E2%29%2Fx%5E2-4y%5E2%2Fx%5E2%2B3xy%2B2y%5E2%E5%B9%B6%E6%B1%82%E5%87%BAx%2Cy%E6%BB%A1%E8%B6%B32%5E2%2B3xy-5y%5E2%3D0%E6%97%B6%2C%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BC)
化简下面代数式(x+y/x-y+4xy/y^2-x^2)/x^2-4y^2/x^2+3xy+2y^2并求出x,y满足2^2+3xy-5y^2=0时,代数式的值
化简下面代数式(x+y/x-y+4xy/y^2-x^2)/x^2-4y^2/x^2+3xy+2y^2并求出x,y满足2^2+3xy-5y^2=0时,代数式的值
化简下面代数式(x+y/x-y+4xy/y^2-x^2)/x^2-4y^2/x^2+3xy+2y^2并求出x,y满足2^2+3xy-5y^2=0时,代数式的值
(x+y/x-y+4xy/y²-x²)/x²-4y²/x²+3xy+2y²
分子A=(x+y)/(x-y)+(4xy)/(y²-x²)
=[(x+y)²-4xy]/(x²-y²)
=(x-y)²/(x²-y²)
=(x-y)/(x+y)
分母B=(x²-4y²)/(x²+3xy+2y²)
=[(x-2y)(x+2y)]/[(x+y)(x+2y)]
=(x-2y)/(x+y)
A/B=[(x-y)/(x+y)]/[(x-2y)/(x+y)]
=(x+y)/(x-2y)
当2x²+3xy-5y²=0时,有(2x+5y)(x-y)=0,即2x+5y=0或x-y=0,显然后者不合题意,故有
x=-5/2y,代入(x+y)/(x-2y)可得原式的值=5/12