一道今天内要答案的数学题,会的帮个忙捏,鹅
4个回答

1/(a+b)+2a/(a^2+b^)+4a^3/(a^4+b^)-8a^7/(a^8-b^8)

a^8-b^8=(a^4+b^4)(a^4-b^4)

=(a^4+b^4)(a^2+b^2)(a^2-b^2)

=(a^4+b^4)(a^2+b^2)(a-b)(a+b)

1/(a+b)+2a/(a^2+b^2)+4a^3/(a^4+b^4)-8a^7/(a^8-b^8)

=1/(a+b)+2a/(a^2+b^2)+(4a^3(a^4-b^4)/(a^8-b^8)-8a^7/(a^8-b^8)

=1/(a+b)+2a/(a^2+b^2)-(4a^3(a^4+b^4)/(a^8-b^8)

=1/(a+b)+2a/(a^2+b^2)-4a^3/(a^4-b^4)

=1/(a+b)+2a(a^2-b^2)/(a^4-b^4)-4a^3/(a^4-b^4)

=1/(a+b)-2a(a^2+b^2)/(a^4-b^4)

=1/(a+b)-2a/(a^2-b^2)

=(a-b)/(a^2-b^2)-2a/(a^2-b^2)

=(a-b-2a)/(a^2-b^2)

=-(a+b)/(a^2-b^2)

=b-a