化简[6(x-2)²+12(x+2)(x-2)-3(x-1)²(x-2)]÷[3(2-x)]要步骤一步一步的做

化简[6(x-2)²+12(x+2)(x-2)-3(x-1)²(x-2)]÷[3(2-x)]要步骤一步一步的做
化简[6(x-2)²+12(x+2)(x-2)-3(x-1)²(x-2)]÷[3(2-x)]要步骤一步一步的做

化简[6(x-2)²+12(x+2)(x-2)-3(x-1)²(x-2)]÷[3(2-x)]要步骤一步一步的做
解
[6(x-2)²+12(x+2)(x-2)-3(x-1)²(x-2)]÷[3(2-x)]
=3(x-2)[2(x-2)+4(x+2)-(x-1)²]÷[-3(x-2)]
=-[2(x-2)+4(x+2)-(x-1)²]
=-(2x-4+4x+8-x²+2x-1)
=-(8x-x²+3)
=x²-8x-3

=【3（x-2）×2（x-2）+3（x-2）×4（x+2）-3（x-2）×（x-1）²】÷【3（2-x）】
=3（x-2）【2（x-2）+4（x+2）-（x-1）²】÷【-3（x-2）】
= -2（x-2）-4（x+2）+（x-1）²
= x²-8x-3