What is (x-2)/(sqrt(x)+\sqrt{2)} ?

The solution to (x-2)/(sqrt(x)+\sqrt{2)} is sqrt(x)-sqrt(2)

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simplify (x-2)/(sqrt(x)+\sqrt{2)}

simplify

\frac{x - 2}{x + 2}

x - 2

Solution steps

\frac{x - 2}{x + 2}

Multiply by the conjugate

\frac{x - 2}{x - 2}

= \frac{( x - 2 ) ( x - 2 )}{( x + 2 ) ( x - 2 )}

(x + 2) (x - 2) = x - 2

= \frac{( x - 2 ) ( x - 2 )}{x - 2}

Cancel the common factor:

x - 2

= x - 2

\frac{7 ^{- 5}}{7 ^{3}}

(\frac{3}{2} 3^{6} 4^{- 6})^{2}

\frac{5 - i}{5 + i}

3^{8} \cdot 3^{5}

(\frac{1}{x - 2})^{2} + 2

What is (x-2)/(sqrt(x)+\sqrt{2)} ?
The solution to (x-2)/(sqrt(x)+\sqrt{2)} is sqrt(x)-sqrt(2)