What is (3sqrt(3))/(2sqrt(3)-\sqrt{6)} ?

The solution to (3sqrt(3))/(2sqrt(3)-\sqrt{6)} is (6+3sqrt(2))/2

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simplify (3sqrt(3))/(2sqrt(3)-\sqrt{6)}

simplify

\frac{3 3}{2 3 - 6}

\frac{6 + 3 2}{2}

Decimal Notation

5.12132 \dots

Solution steps

\frac{3 3}{2 3 - 6}

Multiply by the conjugate

\frac{2 3 + 6}{2 3 + 6}

= \frac{3 ( 2 3 + 6 ) 3}{( 2 3 - 6 ) ( 2 3 + 6 )}

Expand

3 (23 + 6) : 63 + 36

Expand

(23 - 6) (23 + 6) : 6

= \frac{( 6 3 + 3 6 ) 3}{6}

Factor the number:

6 = 3 \cdot 2

= \frac{( 6 3 + 3 6 ) 3}{3 \cdot 2}

Apply radical rule:

a = a a

3 = 33

= \frac{( 6 3 + 3 6 ) 3}{3 3 \cdot 2}

Cancel the common factor:

3

= \frac{6 3 + 3 6}{3 \cdot 2}

Factor out common term

3 : 3 (23 + 6)

= \frac{3 ( 2 3 + 6 )}{3 \cdot 2}

Apply radical rule:

a = a a

3 = 33

= \frac{3 3 ( 2 3 + 6 )}{3 \cdot 2}

Cancel the common factor:

3

= \frac{3 ( 2 3 + 6 )}{2}

3 (23 + 6) = 6 + 32

= \frac{6 + 3 2}{2}

\frac{24}{3.2 \times 2}

364

(x + 8) (8 x + 2)

\frac{1}{18} + \frac{1}{12}

- 54 + - 150 - - 24

What is (3sqrt(3))/(2sqrt(3)-\sqrt{6)} ?
The solution to (3sqrt(3))/(2sqrt(3)-\sqrt{6)} is (6+3sqrt(2))/2