Question

1/（a-b）+1/（a+b）+2a/（a²+b²）+4a²/（a四次方+b四次方）

Answer 1

因为

(a+b)(a-b)=a²-b²

(a²-b²)(a²+b²)=a^4-b^4

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

所以

[1/(a-b)]+[1/(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)]

=[4a^3/(a^4-b^4)]+[4a^3/(a^4+b^4)]

=8a^7/(a^8-b^8)