Question

化简：[a平方/(a+2)+2]×[1/(a平方-2a)-12/(a四次方-8a)-2/(a三次方+2a平方+4a)]

Answer 1

本题要用到立方差公式： a³-b³=(a-b)(a²+ab+b²)

原式=[a²/(a+2)+2(a+2)/(a+2)]×{ 1/[a(a-2)]-12/[a(a³-8)]-2/[a(a²+2a+4)] }

=[(a²+2a+4)/(a+2)]×{ 1/[a(a-2)]-12/[a(a-2)(a²+2a+4)]-2/[a(a²+2a+4)] }

=[(a²+2a+4)/(a+2)]×{ (a²+2a+4)/[a(a-2)(a²+2a+4)]-12/[a(a-2)(a²+2a+4)]-2(a-2)/[a(a-2)(a²+2a+4)] }

=[(a²+2a+4)/(a+2)]×{ [(a²+2a+4)-12-2(a-2)]/[a(a-2)(a²+2a+4)] }

=[1/(a+2)]×{ (a²+2a+4-12-2a+4)/[a(a-2)] }

=[1/(a+2)]×{ (a²-4)/[a(a-2)] }

=[1/(a+2)]×{ (a+2)(a-2)/[a(a-2)] }

=1/a