Math problem with limits?

lim x→−∞
3x^8 −2x^4 + 1 / −7x^12 −5x^3 + x
Answer is 0.What i do is differentiate it first.Factor the top part like 8x^3(3x^4-1).I make a reduction with the bottom part and removing all the top x.Then we have constans over infinity which is 0.Am i stupid ? Is that how you do it ?
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