What is (x-sqrt(2x))/(x+sqrt(2x)) ?

The solution to (x-sqrt(2x))/(x+sqrt(2x)) is ((sqrt(x)-sqrt(2))^2)/(x-2)

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simplify (x-sqrt(2x))/(x+sqrt(2x))

simplify

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

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

Solution steps

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

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

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

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

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

Factor

x - 2 x : x (x - 2)

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

Factor

x + 2 x : x (x + 2)

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

Cancel the common factor:

x

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

Rationalize

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

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

x y + 2 x + y + 2

x + 19 x + 21

2^{2} - x^{2}

6 x + 42

6 x + 48

What is (x-sqrt(2x))/(x+sqrt(2x)) ?
The solution to (x-sqrt(2x))/(x+sqrt(2x)) is ((sqrt(x)-sqrt(2))^2)/(x-2)