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  • 計(jì)算:[(x+2)/(x+3) - (x+1)/(x+2) + (x+4)/(x+5) - (x+3)/(x+4) / (x^2 + 7x + 13)/(x^2 + 8x + 15)

    計(jì)算:[(x+2)/(x+3) - (x+1)/(x+2) + (x+4)/(x+5) - (x+3)/(x+4) / (x^2 + 7x + 13)/(x^2 + 8x + 15)
    數(shù)學(xué)人氣:682 ℃時(shí)間:2019-12-13 17:43:10
    優(yōu)質(zhì)解答
    [(x+2)/(x+3) - (x+1)/(x+2) + (x+4)/(x+5) - (x+3)/(x+4)] / (x^2 + 7x + 13)/(x^2 + 8x + 15)
    =[-1/(x+3)+1/(x+2)-1/(x+5)+1/(x+4)] / (x^2 + 7x + 13)/(x^2 + 8x + 15)
    =[(1/(x+4)-1/(x+3))+(1/(x+2)-1/(x+5))]/ (x^2 + 7x + 13)/(x^2 + 8x + 15)
    =(-1/(x^2+7x+12)+3/(x^2+7x+10))/ (x^2 + 7x + 13)/(x^2 + 8x + 15)
    =[(2x^2+14x+26)/(x+2)(x+3)(x+4)(x+5)]/ [(x^2 + 7x + 13)/(x+3)(x+5)]
    =2/(x+2)(x+4)
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