化简:1/(x-1)-1/(x+1)-2/(x²+1)-4/(x^4+1)-8/(x^8+1)

问题描述:

化简:1/(x-1)-1/(x+1)-2/(x²+1)-4/(x^4+1)-8/(x^8+1)

式子化简,第一步:1/(x-1) - 1/(x+1) = ((x+1)-(x-1))/(x^2 - 1) = 2 / (x^2 - 1)第二步:2/(x^2 - 1) - 2/(x^2 +1) = 4/(x^4 - 1)第三步:4/(x^4 - 1) - 4/(x^4 + 1) = 8/(x^8 - 1)第四步:8/(x^8 - 1) - 8/(x^8 + 1) = 16/(x^8 - 1)所以原式化简得 16/(x^8 - 1).