Fractions of the limits

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Compute this fraction considering a=const.a=const.

(limx1(x+3)a2+1)2limx2(x+3)(a4+2a2+1)=\dfrac{(\lim\limits_{x\to1} \dfrac{(x+3)}{a^2+1})^2}{\lim\limits_{x\to2} (x+3)}(a^4+2a^2+1)=

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