{1} 1/(a-x)-1/(a+x)-2x/(a^2+x^2)-4x^3/(a^4+x^4)-8x^7/(x^8-a^8){2} 1/{x(x+1)}+1/{(x+1)(x+2)}+1/{(x+2)(x+3)}+1/{(x+3)(x+4)}
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![{1} 1/(a-x)-1/(a+x)-2x/(a^2+x^2)-4x^3/(a^4+x^4)-8x^7/(x^8-a^8){2} 1/{x(x+1)}+1/{(x+1)(x+2)}+1/{(x+2)(x+3)}+1/{(x+3)(x+4)}](/uploads/image/z/168029-53-9.jpg?t=%7B1%7D+1%2F%28a-x%29-1%2F%28a%2Bx%29-2x%2F%28a%5E2%2Bx%5E2%29-4x%5E3%2F%28a%5E4%2Bx%5E4%29-8x%5E7%2F%28x%5E8-a%5E8%29%7B2%7D+1%2F%7Bx%28x%2B1%29%7D%2B1%2F%7B%28x%2B1%29%28x%2B2%29%7D%2B1%2F%7B%28x%2B2%29%28x%2B3%29%7D%2B1%2F%7B%28x%2B3%29%28x%2B4%29%7D)
{1} 1/(a-x)-1/(a+x)-2x/(a^2+x^2)-4x^3/(a^4+x^4)-8x^7/(x^8-a^8){2} 1/{x(x+1)}+1/{(x+1)(x+2)}+1/{(x+2)(x+3)}+1/{(x+3)(x+4)}
{1} 1/(a-x)-1/(a+x)-2x/(a^2+x^2)-4x^3/(a^4+x^4)-8x^7/(x^8-a^8)
{2} 1/{x(x+1)}+1/{(x+1)(x+2)}+1/{(x+2)(x+3)}+1/{(x+3)(x+4)}
{1} 1/(a-x)-1/(a+x)-2x/(a^2+x^2)-4x^3/(a^4+x^4)-8x^7/(x^8-a^8){2} 1/{x(x+1)}+1/{(x+1)(x+2)}+1/{(x+2)(x+3)}+1/{(x+3)(x+4)}
1、很好做呦:
首先是找规律:
1/(a-x)-1/(a+x)=2x/(a^2-x^2),然后和后面的一个式子再合并,
2x/(a^2-x^2)-2x/(a^2+x^2)=4x^3/(a^4-x^4),
4x^3/(a^4-x^4)-4x^3/(a^4+x^4)=8x^7/(x^8-a^8),
前面四个式子的结果是8x^7/(x^8-a^8)和最后一个式子相同,则平方为64x^14/(x^8-a^8)^2,即为最后结果.
2、第一题是合并,这一题是分解.
1/{x(x+1)}+1/{(x+1)(x+2)}+1/{(x+2)(x+3)}+1/{(x+3)(x+4)}=
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=
1/x-1/(x+4)= 4/x(x+4).