Question

一道初一分式题a为整数,(a2-4a+4)(a^3+2) (a+1)(a2-a+1)且----------------

Answer 1

原式=(a-2)²(a³+2)/[(a-2)(a²+2a+4)-6a(a-2)]-(a+1)(a²-a+1)/(a-2)

=(a-2)²(a³+2)/[(a-2)(a²-4a+4)]-(a+1)(a²-a+1)/(a-2)

=(a-2)²(a³+2)/(a-2)³-(a+1)(a²-a+1)/(a-2)

=(a³+2)/(a-2)-(a³+1)/(a-2)

=(a³+2-a³-1)/(a-2)

=1/(a-2)

是正整数

所以a-2是1的约数

所以a-2=1

a=3