GMAT Roots: If x>0, then 1/(√(2x)+√x)=

If x > 0, then \frac{1}{2 x + x} =

rootssimplifications & cancellations

Explanation	Calculations	Help
$We multiply numerator and denominator by the expression 2 x - x to create a difference of squares in the denominator.$	$\frac{1}{2 x + x} \times \frac{2 x - x}{2 x - x}$
$We simplify the denominator by applying the difference of squares formula.$	$\frac{2 x - x}{2 x - x}$
$We factor out x from the numerator.$	$\frac{( 2 - 1 ) x}{x}$
$We cancel one factor of x in the numerator and denominator to obtain the final expression.$	$\frac{( 2 - 1 ) x}{x x} = \frac{2 - 1}{x}$

(\sqrt2-1)/(\sqrtx) (D)

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