((4/a^2+12a+27)+(5/a^2+10a+21))

Question

Perform the indicated operation

Answer 1

4/(a²+12a+27)=4/((a+9)(a+3)); 5/(a²+10a+21)=5/((a+7)(a+3)).

So sum is:

4/((a+9)(a+3))+5/((a+7)(a+3))=(1/(a+3))(4/(a+9)+5/(a+7))=

(1/(a+3))(4a+28+5a+45)/((a+7)(a+9))=

(1/(a+3))(9a+73)/(a²+16a+63)=

(9a+73)/(a³+16a²+63a+3a²+48a+189)=(9a+73)/(a³+19a²+111a+189).

Could also be written (9a+73)/((a+3)(a+7)(a+9)).