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

Learn how to solve limits by rationalizing problems step by step online. Find the limit of (x(x+2)^(1/2)-xx^(1/2))/x as x approaches infinity. When multiplying exponents with same base you can add the exponents: -x\sqrt{x}. 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.