分式的计算.求详细解答、解题思路及方法

1个回答

  • 解(1):

    原式=3/(x+2)+1/(2-x)+2x/(x²-4) 通分,最简公分母是(x-2)(x+2)

    =3(x-2)/[(x-2)(x+2)]-(x+2)/[(x-2)(x+2)]+2x/[(x-2)(x+2)]

    =[3(x-2)-(x+2)+2x]/[(x-2)(x+2)]

    =(3x-6-x-2+2x)/[(x-2)(x+2)]

    =(4x-8)/[(x-2)(x+2)]

    =4(x-2)/[(x-2)(x+2)] 约分

    =4/(x+2)

    解(2):

    原式=[(x+1)/(x-1)-(x-1)/(x+1)]÷[x/(x²-1)] 前面括号内通分

    =[(x+1)²/(x²-1)-(x-1)²/(x²-1)]×[(x²-1)/x]

    ={[(x+1)²-(x-1)²]/(x²-1)}×[(x²-1)/x] 约分,合并

    =(x²+2x+1-x²+2x-1)/x

    =4x/x

    =4

    解(3):

    原式=[(a+2)/(a²-2a)-(a-1)/(a²-4a+4)]÷[(4-a)/(a²-2a)] 分解因式

    ={(a+2)/[a(a-2)]-(a-1)/(a-2)²}÷{(4-a)/[a(a-2)]} 通分

    ={(a+2)(a-2)/[a(a-2)²]-a(a-1)/[a(a-2)²]}×[a(a-2)/(4-a)]

    ={[(a+2)(a-2)-a(a-1)]/[a(a-2)²]}×[a(a-2)/(4-a)] 约分,合并

    =[(a²-4-a²+a)/(a-2)]×[1/(4-a)]

    =[(a-4)/(a-2)]×[-1/(a-4)] 约分

    =-1/(a-2)