Question

化简求值：（x^2-6x+9/x^2+4x+4）/（x^2-9/x）*(x^2+3x/3-x),其中x=2

Answer 1

解：
原式=[(x²-6x+9)/(x²+4x+4)]÷[(x²-9)/x]×[(x²+3x)/(3-x)]
=[(x-3)²/(x+2)²]÷[(x+3)(x-3)/x]×[-x(x+3)/(x-3)]
=[(x-3)²/(x+2)²]×{x/[(x+3)(x-3)]×[-x(x+3)/(x-3)]
=-x²/(x+2)²
=-2²/(2+2)²
=-4/16
=-1/4

追问

还有个：先化简 再求值：(m-2/m^2+2m+1)/(1/m^2+m)*(m^2-1/2-m)，其中m=-1/2

追答

可以了，同学：
原式=[(m-2)/(m+1)²]÷{1/[m(m+1)]}×[-(m+1)(m-1)/(m-2)]
=[(m-2)/(m+1)²]×m(m+1)×[-(m+1)(m-1)/(m-2)]
=-m(m-1)
=(1/2)×(-1/2-1)
=(1/2)×(-3/2)
=-3/4