Solve for: limit as x approaches-sqrt(2) of (x^2-sqrt(2)x+sqrt(3)x-sqrt(6))/(x-sqrt(2))

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Expression: $\lim _{x\to -\sqrt{2}}(\frac{x^{2}-\sqrt{2}x+\sqrt{3}x-\sqrt{6}}{x-\sqrt{2}})$

Plug in the value $ x=-\sqrt{2}$

$=\frac{(-\sqrt{2})^{2}-\sqrt{2}(-\sqrt{2})+\sqrt{3}(-\sqrt{2})-\sqrt{6}}{-\sqrt{2}-\sqrt{2}}$

Simplify $\frac{(-\sqrt{2})^{2}-\sqrt{2}(-\sqrt{2})+\sqrt{3}(-\sqrt{2})-\sqrt{6}}{-\sqrt{2}-\sqrt{2}}:{\quad}\frac{\sqrt{6}-2}{\sqrt{2}}$

$=\frac{\sqrt{6}-2}{\sqrt{2}}$

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