Let $x$ be a positive real number. Find the maximum possible value of $$\frac{x^2+2-\sqrt{x^4+4}}{x}.$$
Question:
Let $x$ be a positive real number. Find the maximum possible value of $$\frac{x^2+2-\sqrt{x^4+4}}{x}.$$
Answer:
Let's think step by step.

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2\sqrt{2}-2
Let $x$ be a positive real number. Find the maximum possible value of $$\frac{x^2+2-\sqrt{x^4+4}}{x}.$$
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