作业帮化简：(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 11:11:27
![化简：(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)](/uploads/image/z/2757727-55-7.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9A%28x-y%29%2F%282x%2B1%29+%2A+%5B%282x%2B1%29%2F%28x%2By%29+-+%282xy%2By%29%2F%28y%E6%96%B9%EF%BC%8Dx%E6%96%B9%29%5D%2By%2F%28x%2By%29)
化简：(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)
化简：(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)
化简：(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)
[(2x+1)/(x+y) - (2xy+y)/(y方－x方)]
=[(2x+1)(y-x)/(y^2-x^2) - y(2x+1)/(y^2-x^2)]
=(2x+1)(y-x-y)/(y^2-x^2)
=-x(2x+1)/(y^2-x^2)
(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)
=(x-y)/(2x+1) * [-x(2x+1)/(y^2-x^2)]+y/(x+y)
=(x-y)/(2x+1) * [x(2x+1)/(x-y)(x+y))]+y/(x+y)
=x/(x+y)+y/(x+y)
=1
：(x-y)/(2x+1) * [(2x+1)/(x+y) - (2xy+y)/(y方－x方)]+y/(x+y)
=(x-y)/(2x+1) * (2x+1)/(x+y)-(x-y)/(2x+1) * (2xy+y)/(y方－x方)+y/(x+y)
=(x-y)/(x+y)+y/（x+y)+y/（x+y）
=1