先化简,再求值:x^2-4分之x^2-2x÷(x-2-x+2分之2x-4),其中x=2+根号2_数学解答

先化简,再求值:x^2-4分之x^2-2x÷(x-2-x+2分之2x-4),其中x=2+根号2

人气：109 ℃　时间：2019-10-19 13:35:19

解答

(x^2-2x)/(x^2-4)÷[(x-2)-(2x-4)/(x+2)]
=x(x-2)/(x-2)(x+2)÷[(x-2)-(2x-4)/(x+2)]
=x/(x+2)÷[(x-2)-(2x-4)/(x+2)]
=x/(x+2)÷[(x-2)(x+2)-2(x-2)]/(x+2)
=x/(x+2)÷[(x-2)(x+2-2)]/(x+2)
=x/(x+2)÷x(x-2)/(x+2)
=x/(x+2)*(x+2)/x(x-2)
=1/(x-2)
=1/(2+√2-2)
=1/√2
=√2/2