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# Simplify the expression $\frac{\sqrt{x+2}-\sqrt{2}}{x}$

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##  Step-by-step Solution 

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• Choose an option
• Write in simplest form
• Solve by quadratic formula (general formula)
• Find the derivative using the definition
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
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##  Final answer to the problem

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## Limit

$\lim_{x\to0}\left(\frac{\sqrt{x+2}-\sqrt{2}}{x}\right)=\frac{1}{2\sqrt{2}}$ See step-by-step solution

## Derivative

$\frac{d}{dx}\left(\frac{\sqrt{x+2}-\sqrt{2}}{x}\right)=\frac{x-2\left(x+2\right)+\sqrt{2}\cdot 2\sqrt{x+2}}{2\sqrt{x+2}x^2}$ See step-by-step solution

## Integral

$\int\frac{\sqrt{x+2}-\sqrt{2}}{x}dx=\sqrt{\left(2\right)^{3}}+2\sqrt{x+2}-2\sqrt{2}\ln\left|\sqrt{x+2}+\sqrt{2}\right|+C_0$ See step-by-step solution

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more