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)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)
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![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)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)](/uploads/image/z/2586622-22-2.jpg?t=%E8%AE%A1%E7%AE%971%2F%28m-n%29-1%2F%28m%2Bn%29-2n%2F%28m%5E2%2Bn%5E2%29-4n%5E3%2F%28m%5E4%2Bn%5E4%29-8n%5E7%2F%28m%5E8%2Bn%5E8%29-16n%5E15%2F%28m%5E16%2Bn%5E16%29%2B32n%5E31%28n%5E32-m%5E32%29)
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)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)
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)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)
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)-16n^15/(m^16+n^16)+32n^31(n^32-m^32)
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