作业帮化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/26 01:12:35
![化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]](/uploads/image/z/3679102-46-2.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9A%5B%28x%2B2%29%2F%28x%5E2-4%29-%282x-5%29%2F%28x-4x%2B4%29%5D%C3%B7%5B%28x-3%29%2F%28x-2%29%5D)
化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]
化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]
化简：[(x+2)/(x^2-4)-(2x-5)/(x-4x+4)]÷[(x-3)/(x-2)]
解
原式
=[(x+2)/(x-2)(x+2)-(2x-5)/(x-2)²]×(x-2)/(x-3)
=[1/(x-2)-(2x-5)/(x-2)²]×(x-2)/(x-3)
=1/(x-3)-(2x-5)/(x-2)(x-3)
=(x-2)/(x-2)(x-3)-(2x-5)/(x-2)(x-3)
=(x-2-2x+5)/(x-2)(x-3)
=(-x+3)/(x-2)(x-3)
=-1/(x-2)
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