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

0.42264 \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}

\frac{4 + 3 i}{- 10 + i}

(5 a - 7 b) (a + 3 b)

(x^{2} - 3)^{2} - 3

\frac{4 x ^{2}}{x ^{2}}

(5 x - x^{2} + 3) + (12 - 7 x - 9 x^{2})