Help me solve this difficult problem a^4+3/a-2 * a^5-2/a-2?

a^4+3/a-2 x a^5-2/a-2

=(a^4+3)(a^5-2)
---------------------- answer
(a-2)^2

May I suggest that your biggest problem is presentation of question. Your question may be read (misread) in many ways.

SHOULD , I suspect, be meant to read as :-

[ ( a^4 + 3 ) / (a - 2) ] [ (a^5 - 2) / (a - 2) ]

( a^4 + 3 ) (a^5 - 2)
----------------------------
(a - 2) (a - 2)

OR , if desired :-

a^9 + 3 a^5 - 2 a^4 - 6
------------------------------
( a - 2 ) ²

(a^4 + 3)/(a - 2) * (a^5 - 2)/(a - 2)
= (a^4 + 3)(a^5 - 2)/(a - 2)^2

you should really use brackets! because I can't really get the exercise like this>[a^(4+3/a-2)]*[a^(5-2/a-2)]=a^(4+5+3/a-2 - 2/a-2)= a^[9(a-2)+1]/a-2=a^[(9a-17)/a-2]

no