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[tex]\frac{2a^4+3a^3+2a+3}{(a^2-a+1)(2a+3)}[/tex]

(2а⁴+3а³+2а+3)/(а²-а+1)(2а+3)(а³(2а+3)+(2а+3))/(а²-а+1)(2а+3)=(2а+3)(а³+1)/(а²-а+1)(2а+3)=(а³+1)/(а²-а+1)=(а+1)(а²-а+1)/(а²-а+1)=а+1