分式的加减计算:(1/x-1)+(1/x+1)-(2x/x^2+1)-(4x/x^4+1)-(8x/x^8+1) 注:“
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分式的加减计算:(1/x-1)+(1/x+1)-(2x/x^2+1)-(4x/x^4+1)-(8x/x^8+1) 注:“/”指除号.
![分式的加减计算:(1/x-1)+(1/x+1)-(2x/x^2+1)-(4x/x^4+1)-(8x/x^8+1) 注:“](/uploads/image/z/15419048-32-8.jpg?t=%E5%88%86%E5%BC%8F%E7%9A%84%E5%8A%A0%E5%87%8F%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881%2Fx-1%29%2B%281%2Fx%2B1%29-%282x%2Fx%5E2%2B1%29-%284x%2Fx%5E4%2B1%29-%288x%2Fx%5E8%2B1%29+%E6%B3%A8%EF%BC%9A%E2%80%9C)
(1/x-1)+(1/x+1)-(2x/x^2+1)-(4x/x^4+1)-(8x/x^8+1)
=(x+1+x-1)/(x^2-1)-(2x/x^2+1)-(4x/x^4+1)-(8x/x^8+1)
=[2x(x^2+1)-2x(x^2-1)]/(x^4-1)-(4x/x^4+1)-(8x/x^8+1)
=[4x(x^4+1)-4x(x^4-1)]/(x^8-1) )-(8x/x^8+1)
=[8x(x^8+1)-8x(x^8-1)]/(x^16-1)
=16x/(x^16-1)
=(x+1+x-1)/(x^2-1)-(2x/x^2+1)-(4x/x^4+1)-(8x/x^8+1)
=[2x(x^2+1)-2x(x^2-1)]/(x^4-1)-(4x/x^4+1)-(8x/x^8+1)
=[4x(x^4+1)-4x(x^4-1)]/(x^8-1) )-(8x/x^8+1)
=[8x(x^8+1)-8x(x^8-1)]/(x^16-1)
=16x/(x^16-1)
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