Question

先化简,再求值[(a^3+2a^2+4a)/(a-2)(a^2+2a+4)]-10/(a^2+a-6)除以[1- 21/

Answer 1

[(a^3+2a^2+4a)/(a-2)(a^2+2a+4)]-10/(a^2+a-6)除以[1- 21/(a^2-4)]*(a+3)/(a-2)

=[a(a^2+2a+4)/(a-2)(a^2+2a+4)]-10/(a^2+a-6)*[(a^2-4)/(a^2-4)-21]*(a+3)/(a-2)

=a/(a-2)-10/(a+3)(a-2)*[(a-2)(a+2)/(a^2-4)-21]*(a+3)/(a-2)

=a/(a-2)-10(a+2)/(a+3)(a^2+17)*(a+3)/(a-2)

=a/(a-2)-10(a+2)/(a^2+17)(a-2)

=(a(a^2+17)-10(a+2))/(a^2+17)(a-2)

=(a^3+17a-10a-20)/(a^2+17)(a-2)

=(a^3+7a-20)/(a^2+17)(a-2)

=((1/2)^3+7*1/2-20)/((1/2)^2+17)(1/2-2)

=131/207