计算： 1）1-(x-1/1-x)^2÷x^2-x+1/1-2x+x^2 2）(1+4/a^2-4)÷a/a+2 3)[1/(a+2)+1]·a^4-4/a^2+3a

来源：学生作业帮助网编辑：作业帮时间：2024/11/15 01:50:19

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计算： 1）1-(x-1/1-x)^2÷x^2-x+1/1-2x+x^2 2）(1+4/a^2-4)÷a/a+2 3)[1/(a+2)+1]·a^4-4/a^2+3a
计算： 1）1-(x-1/1-x)^2÷x^2-x+1/1-2x+x^2 2）(1+4/a^2-4)÷a/a+2 3)[1/(a+2)+1]·a^4-4/a^2+3a

计算： 1）1-(x-1/1-x)^2÷x^2-x+1/1-2x+x^2 2）(1+4/a^2-4)÷a/a+2 3)[1/(a+2)+1]·a^4-4/a^2+3a
(1).1-(x-1/1-x)^2÷x^2-x+1/1-2x+x^2
=1-[x(1-x)-1]²/(1-x)²·(1-2x+x² )/(x²-x+1)
=1-(x-x²-1)/(1-x)²·(1-2x+x² )/(x²-x+1)
=1+(x²-x+1)/(x-1)²·(x-1)²/(x²-x+1)
=1+1
=2
(2)）[1+4/(a^2-4)]÷a/(a+2)
=a²/(a²-4)·(a+2)/a
=a/(a-2)
(3)题目是不是打错了?应该是
[1/(a+2)+1]·(a2-4)/(a^2+3a)
=(a+3)/(a+2)·（a+2)（a-2)/a(a+3)
=(a-2)/a

(1).1-(x-1/1-x)^2÷x^2-x+1/1-2x+x^2
=1-[x(1-x)-1]²/(1-x)²·(1-2x+x² )/(x²-x+1)
=1-(x-x²-1)/(1-x)²·(1-2x+x² )/(x²-x+1)
=1+(x²-x+1)/(x-1)²·(x-1)²/(x²-x+1)
=1+1
=2

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