If x0, then 1sqrt(2 x)+sqrt(x)=

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If x>0, then 1sqrt(2 x)+sqrt(x)=

GMAT Panda · Accepted Answer

D We multiply numerator and denominator by the expression sqrt(2x)-sqrt(x) to create a difference of squares in the denominator. 1sqrt(2x)+sqrt(x) sqrt(2x)-sqrt(x)sqrt(2x)-sqrt(x) We simplify the denominator by applying the difference of squares formula. sqrt(2x)-sqrt(x)2x - x We factor out sqrt(x) from the numerator. (sqrt(2)-1)sqrt(x)x We cancel one factor of sqrt(x) in the numerator and denominator to obtain the final expression. (sqrt(2)-1)sqrt(x)sqrt(x)sqrt(x) = sqrt(2)-1sqrt(x)

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

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