Question

X平方+X-6分之4X平方+12X除(X+2分之X-2-X-2分之X+2)其中X=-3又2分之1

Answer 1

[(4x²+12x)/(x²+x-6)]÷[(x-2)/(x+2)-(x+2)/(x-2)]
=[4x(x+3)/(x+3)(x-2)]÷[(x-2)²-(x+2)²]/(x+2)(x-2)
=[4x/(x-2)]÷[-8x/(x+2)(x-2)]
=[4x/(x-2)]×[(x+2)(x-2)/(-8x)]
=-(x+2)/2
当x=-3又2分之1时，原式=-(-1又2分之1)/2=3/4

Answer 2

解：原式为：[(4x²+12x)/(x²+x-6)]÷[(x-2)/(x+2)-(x+2)/(x-2)]，x=-3½。
原始化为：{4x(x+3)/[(x+3)(x-2)]}÷{(x-2)²/[(x+2)*(x-2)]-(x+2)²/(x+2)*(x-2)]}
＝{4x(x+2)/[(x+2)*(x-2)]}*{[(x+2)*(x-2)]/[(x+2)²-(x-2)²]}
＝4x(x+2)/[(x+2)²-(x-2)²]=4x(x+2)/8x=(x+2)/2①，将x=-3½代入①式得：原式值为：-0.75或-3/4。