代数式1/(x-1)+1/(x+1)+2x/(x²+1)+4x³/(x⁴+1)
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代数式1/(x-1)+1/(x+1)+2x/(x²+1)+4x³/(x⁴+1)
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![代数式1/(x-1)+1/(x+1)+2x/(x²+1)+4x³/(x⁴+1)](/uploads/image/z/8065833-33-3.jpg?t=%E4%BB%A3%E6%95%B0%E5%BC%8F1%2F%EF%BC%88x-1%EF%BC%89%2B1%2F%EF%BC%88x%2B1%EF%BC%89%2B2x%2F%EF%BC%88x%26%23178%3B%2B1%EF%BC%89%2B4x%26%23179%3B%2F%EF%BC%88x%26%238308%3B%2B1%EF%BC%89)
1/(x-1)+1/(x+1)+2x/(x²+1)+4x³/(x⁴+1)
=(x+1+x-1)/(x-1)(x+1)+2x/(x²+1)+4x³/(x⁴+1)
=2x/(x²-1)+2x/(x²+1)+4x³/(x⁴+1)
=2x(x²+1+x²-1)/(x²-1)(x²+1)+4x³/(x⁴+1)
=4x³/(x⁴-1)+4x³/(x⁴+1)
=4x³(x⁴+1+x⁴-1)/(x⁴-1)(x⁴+1)
=4x³*2x⁴/[(x⁴)²-1]
=8x^7/(x^8-1)
=(x+1+x-1)/(x-1)(x+1)+2x/(x²+1)+4x³/(x⁴+1)
=2x/(x²-1)+2x/(x²+1)+4x³/(x⁴+1)
=2x(x²+1+x²-1)/(x²-1)(x²+1)+4x³/(x⁴+1)
=4x³/(x⁴-1)+4x³/(x⁴+1)
=4x³(x⁴+1+x⁴-1)/(x⁴-1)(x⁴+1)
=4x³*2x⁴/[(x⁴)²-1]
=8x^7/(x^8-1)
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