Find the limit of $\frac{\sqrt{x+2}-\sqrt{2}}{\sqrt{3}-\sqrt{3+x}}$ as $x$ approaches 0

Learn how to solve product rule of differentiation problems step by step online. Find the limit of ((x+2)^(1/2)-*2^(1/2))/(3^(1/2)-(3+x)^(1/2)) as x approaches 0. Applying rationalisation. Multiply and simplify the expression within the limit. Subtract the values 2 and -2. Multiply the single term \sqrt{x+2}+\sqrt{2} by each term of the polynomial \left(\sqrt{3}-\sqrt{3+x}\right).