tombbs050
幼苗
共回答了16个问题采纳率:100% 举报
(2/(x+3))÷(2/(3-x))+(2x+18/x的平方-9)
=(3-x)/(x+3)+2(x+9)/(x+3)(x-3)
=-(x-3)^2/(x+3)(x-3)+2(x+9)/(x+3)(x-3)
=(2x+18-x^2+6x-9)/(x+3)(x-3)
=-(x^2-8x-9)/(x^2-9)
=-1+8x/(x^2-9)
=-1+8/(x-9/x)是整数
则x-9/x是8的约数
x-9/x=1,-1,2,-2,4,-4,8,-8
则若x=a时x-9/x是整数
则x=-a时x-9/x也是整数
所以所有x的值的和为0
原式=(a+b+a-b)/(a+b)(a-b)+2a/(a^2+b^2)+4a^3/(a^4+b^4)
=2a/(a^2-b^2)+2a/(a^2+b^2)+4a^3/(a^4+b^4)
=2a(a^2+b^2+a^2-b^2)/(a^2-b^2)(a^2+b^2)+4a^3/(a^4+b^4)
=4a^3/(a^4-b^4)+4a^3/(a^4+b^4)
=4a^3*2a^4/(a^4+b^4)(a^4-b^4)
=8a^7/a^8-b^8)
1年前
2