Find the limit of $\frac{6-x}{\sqrt{x^2+3}+\sqrt{x^2-3}}$ as $x$ approaches $\infty $

Learn how to solve limits by direct substitution problems step by step online. Find the limit of (6-x)/((x^2+3)^(1/2)+(x^2-3)^(1/2)) as x approaches infinity. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Rewrite the fraction, in such a way that both numerator and denominator are inside the exponent or radical. Separate the terms of both fractions. Evaluate the limit \lim_{x\to\infty }\left(\frac{\sqrt{\frac{x^2}{\left(6-x\right)^{2}}+\frac{3}{\left(6-x\right)^{2}}}}{\sqrt{\frac{x^2}{\left(\sqrt{x^2+3}+\sqrt{x^2-3}\right)^{2}}+\frac{3}{\left(\sqrt{x^2+3}+\sqrt{x^2-3}\right)^{2}}}}\right) by replacing all occurrences of x by \infty .