计算(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)
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![计算(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)](/uploads/image/z/401687-71-7.jpg?t=%E8%AE%A1%E7%AE%97%281%2Fx%26%23178%3B%2B3x%2B2%29%2B%281%2Fx%26%23178%3B%2B5x%2B6%29%2B%281%2Fx%26%23178%3B%2B7x%2B12%29)
计算(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)
计算(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)
计算(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)
原式=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)
=1/(x+1)-1/(x+4)
=(x+4-x-1)/(x²+5x+4)
=3/(x²+5x+4)