What is (sqrt(12x))/(2+2sqrt(3)) ?

The solution to (sqrt(12x))/(2+2sqrt(3)) is -((sqrt(3)-3)sqrt(x))/2

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simplify (sqrt(12x))/(2+2sqrt(3))

simplify

\frac{12 x}{2 + 2 3}

- \frac{( 3 - 3 ) x}{2}

Solution steps

\frac{12 x}{2 + 2 3}

Factor out common term

2 : 2 (1 + 3)

= \frac{12 x}{2 ( 1 + 3 )}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

12 x = 12 x

= \frac{12 x}{2 ( 1 + 3 )}

Factor

12 : 23

= \frac{2 3 x}{2 ( 1 + 3 )}

Cancel the common factor:

2

= \frac{3 x}{1 + 3}

Cancel

\frac{3 x}{1 + 3} : - \frac{( 3 - 3 ) x}{2}

= - \frac{( 3 - 3 ) x}{2}

5 (3 x - 2)

10 n - 4 n

- 10 + (- 10)

\frac{( f ( x + h ) - f ( x ) )}{h}

4 x + 20 x^{2}

What is (sqrt(12x))/(2+2sqrt(3)) ?
The solution to (sqrt(12x))/(2+2sqrt(3)) is -((sqrt(3)-3)sqrt(x))/2