What is 2/(3-sqrt(3)) ?

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

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simplify 2/(3-sqrt(3))

simplify

\frac{2}{3 - 3}

\frac{3 + 3}{3}

Decimal Notation

1.57735 \dots

Solution steps

\frac{2}{3 - 3}

Multiply by the conjugate

\frac{3 + 3}{3 + 3}

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

Expand

2 (3 + 3) : 6 + 23

Expand

(3 - 3) (3 + 3) : 6

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

Factor out common term

2 : 2 (3 + 3)

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

Factor the number:

6 = 2 \cdot 3

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

Cancel the common factor:

2

= \frac{3 + 3}{3}

+ 3 x^{2} + 39 x + 108

\frac{15}{1000}

9 \times (- 9)

2 lo g_{15} (lo g_{6} (6))

125 h^{3} - 1