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

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Solution

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No formulas were used

î ƒ Limit of this function

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

î ƒ Derivative of this function

$\frac{d}{dx}\left(\frac{\sqrt{x+2}-\sqrt{2}}{x}\right)=\frac{-x-4+2\sqrt{2}\sqrt{x+2}}{2\sqrt{x+2}x^2}$
See step-by-step solution

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$\left(x^3\right)\div\left(x^2-1\right)$

$\frac{2x^2-2y^2}{\sqrt[3]{x+y}}$

$6x^3y^2\div2y$

Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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