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Limit at Infinity with Radicals

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Evaluate the following limit: lim⁡x→∞x2+5x+6−x4x2+3x−2x\lim_{x\to\infty} \frac{\sqrt{x^2+5x+6}-x}{\sqrt{4x^2+3x}-2x}

A

83\frac{8}{3}

B

44

C

103\frac{10}{3}

D

52\frac{5}{2}

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