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Verified answer
[(a³-27)/(3a³-18a²+27a) ] :([(a-3)/(3a+9)] - [(a+3)/ (a²-3a)] - [(3a+3)/(9-a²)])== [(a³-3³)/(3a(a²-6a+9)] :([(a-3)/3(a+3)] - [(a+3)/a(a-3)] - [(3(a+1)/ -(a²-3²)])=
= [ ((a-3)(a²+3a+3²) ) / (3a(a-3)² ] :
: [( a(a-3)(a-3 ) - 3(a+3)(a+3) +3(a+1)*3a) / ( 3а(а-3)(а+3) ) ] =
= [ (a²+3a+9) / (3a(a-3)) ] : [( a(a-3)² -3(a+3)² +9a(a+1))/ (3a(a-3)(a+3)]=
= [(a²+3a+9)/(3a(a-3))] : [(a(a²-6a+9)-3(a²+6a+9) +9a²+9a) / (3a(a²-9))]=
= [ (a²+3a+9)/(3a(a-3))] : [(a³-6a²+9a -3a²-18a-27 +9a²+9a) /(3a(a²-9))]=
= [ (a²+3a+9) / (3a(a-3))] : [(a³ -27) / (3a(a²-9))]=
= [ (a²+3a+9)/ (3a(a-3)) ] : [ ( (a-3)(a²+3a+9)) / (3а(а-3)(а+3))] =
= [ (a²+3a+9) / (3a(a-3)) ] : [ (a²+3a+9) / (3a(a+3)) ] =
= [ (a²+3a+9) / (3a (a-3)) ] * [ (3a(a+3) ) / (a²+3a+9) ]=
= (a+3) / (a-3)
Verified answer
1)(a-3)/3(a+3)-(a+3)/a(a-3)+(3a+3)/(a-3)(a+3)==[(a-3)(a²-3a)-(a+3)(3a+9)+3a(3a+3)]/[3a(a²-9)]=
=(a³-3a²-3a²+9a-3a²-9a-9a-27+9a²+9a)/[3a(a²-9)]=
=(a³-27)/[3a(a²-9)]
2)(a³-27)/[3a(a²-9)]*3a(a+3)(a-3)/(a³-27)=(a+3)/(a-3)