What is 3/(3+sqrt(3)) ?

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

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simplify 3/(3+sqrt(3))

simplify

\frac{3}{3 + 3}

\frac{3 - 3}{2}

Decimal Notation

0.63397 \dots

Solution steps

\frac{3}{3 + 3}

Multiply by the conjugate

\frac{3 - 3}{3 - 3}

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

Expand

3 (3 - 3) : 9 - 33

Expand

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

= \frac{9 - 3 3}{6}

Factor out common term

3 : 3 (3 - 3)

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

Factor the number:

6 = 3 \cdot 2

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

Cancel the common factor:

3

= \frac{3 - 3}{2}

\frac{7 - 6 i}{6 + 9 i}

(- \frac{4}{9}) + (- \frac{6}{18})

5 x + 5 x

20 \cdot \frac{1}{3}

\frac{2}{7 - 11}