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1、(1)计算{(3-x)/(x-2)}/(x-2-(13-4x)/(x-2)) (2) {1+4/(a-2)(a-4+

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/06 23:18:43
1、(1)计算{(3-x)/(x-2)}/(x-2-(13-4x)/(x-2)) (2) {1+4/(a-2)(a-4+4/a)-3}/(1/a²-1)
(1){(3-x)/(x-2)}/(x-2-(13-4x)/(x-2))
  ={(3-x)/(x-2)}/{(x-2)*(x-2)-(13-4x)/(x-2)
  ={(3-x)/(x-2)}/{((x²-4x+4)-(13-4x))/(x-2}
  ={(3-x)/(x-2)}/{(x²-4x+4-13+4x)/(x-2}
  ={(3-x)/(x-2)}/{(x²-9)/(x-2)}
  ={(3-x)/(x-2)}/{(x-3)*(x+3)/(x-2)}
  =(3-x)/(x-2)*(x-2)/(x-3)/(x+3)
  =-(x-3)/(x-3)/(x+3)
  =-1/(x+3)
 (2) {1+4/(a-2)(a-4+4/a)-3}/(1/a²-1)
  = {1+4/(a-2)((a-2)-2/a(a-2))-3}/{(1/a-1)(1/a+1)}
  =(1+4-2/a-3)/{(1/a-1)(1/a+1)}
  =(2-2/a)/{(1/a-1)(1/a+1)}
  =2(1-1/a)/{-(1-1/a)(1/a+1)}
  =-2/(1/a+1)