(2a^2+3a+2)/(a+1)-(a^2-a-5)/(a+2)-(3a^2-4a-5)/(a-2)+(2a^2-8a+5)/(a-3)
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(2a^2+3a+2)/(a+1)-(a^2-a-5)/(a+2)-(3a^2-4a-5)/(a-2)+(2a^2-8a+5)/(a-3)
(2a^2+3a+2)/(a+1)-(a^2-a-5)/(a+2)-(3a^2-4a-5)/(a-2)+(2a^2-8a+5)/(a-3)
(2a^2+3a+2)/(a+1)-(a^2-a-5)/(a+2)-(3a^2-4a-5)/(a-2)+(2a^2-8a+5)/(a-3)
=(2a²+2a+a+1+1)/(a+1)-(a²+2a-3a-6+1)/(a+2)-(3a²-6a+2a-4-1)/(a-2)+(2a²-6a-2a+6-1)/(a-3)
=2a+1+1/(a+1)-a+3-1/(a+2)-3a-2+1/(a-2)+2a-2-1/(a-3)
=1/(a+1)-1/(a+2)+1/(a-2)-1/(a-3)
=1/(a+1)(a+2)-1/(a-2)(a-3)
=[(a-2)(a-3)-(a+1)(a+2)]/ (a+1)(a+2)(a-2)(a-3)
=(a²-5a+6-a²-3a-2)/(a+1)(a+2)(a-2)(a-3)
=(4-8a)/(a+1)(a+2)(a-2)(a-3)
(2a^2+3a+2)/(a+1)-(a^2-a-5)/(a+2)-(3a^2-4a-5)/(a-2)+(2a^2-8a+5)/(a-3)
=2(a+1)-a/(a+1)-(a+2)+(5a+9)/(a+2)-3(a-2)-(8a-17)/(a-2)+2(a-3)+(4a-13)/(a-3)
=-1+1/(a+1)+5-1/(a+2)-8+1/(a-2)+4-1/(a-3)
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(2a^2+3a+2)/(a+1)-(a^2-a-5)/(a+2)-(3a^2-4a-5)/(a-2)+(2a^2-8a+5)/(a-3)
=2(a+1)-a/(a+1)-(a+2)+(5a+9)/(a+2)-3(a-2)-(8a-17)/(a-2)+2(a-3)+(4a-13)/(a-3)
=-1+1/(a+1)+5-1/(a+2)-8+1/(a-2)+4-1/(a-3)
=1/(a-2)+1/(a+1)-1/(a+2)-1/(a-3)
=1/(a+1)(a+2)-1/(a-2)(a-3)
=(a^2-5a+6-a^2-3a-2)/(a+1)(a+2)(a-2)(a-3)
=-4(2a+1)/(a+1)(a+2)(a-2)(a-3)
=(-1-8a)/(a+1)(a+2)(a-2)(a-3)
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