Question

计算1/(m-n)-1/(m+n)-2n/(m^2+n^2)-4n^3/(m^4+n^4)-8n^7/(m^8+n^8)

Answer 1

逐步通分

1/(m-n)-1/(m+n)-2n/(m^2+n^2)-4n^3/(m^4+n^4)-8n^7/(m^8+n^8)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)

=[(m+n)-(m-n)]/(m^2-n^2)-2n/(m^2+n^2)-4n^3/(m^4+n^4)-8n^7/(m^8+n^8)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)

=2n/(m^2-n^2)-2n/(m^2+n^2)-4n^3/(m^4+n^4)-8n^7/(m^8+n^8)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)

=4n^3/(m^4-n^4)-4n^3/(m^4+n^4)-8n^7/(m^8+n^8)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)

=32n^31(m^32-n^32)-32n^31(m^32-n^32)

=0