1) (1+4/a^2-4)* a+2/a
=(a^2-4+4)/(a+2)(a-2)*a+2/a
=a^2/(a+2)(a-2)*a+2/a
=a/a-2
2)求代数式的值:
(x^2/x-1 - 2x/1-x)÷x/x-1 其中x=√3 + 1 [ √=根号。]
解:原式=(x^2/x-1 +2x/x-1)*x-1/x
=x(x+2)/x-1*x-1/x
=x+2
当 x=√3 + 1时,原式=√3 + 1+2=√3 + 3
3)解方程: 1/x-1+ 2x/x+1=2
解:方程两边同乘(x-1)(x+1),得
x+1+2x(x-1)=2(x+1)(x-1)
整理得,-x=-3
所以x=3
检验:当x=3时,(x+1)(x-1)不等于0,所以x=3是原方程的根
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(1+4/a^2-4)* a+2/a
=(a^2-4+4)/(a+2)(a-2)*a+2/a
=a^2/(a+2)(a-2)*a+2/a
=a/a-2