What is 3/(6+sqrt(3)) ?

The solution to 3/(6+sqrt(3)) is (6-sqrt(3))/(11)

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simplify 3/(6+sqrt(3))

simplify

\frac{3}{6 + 3}

\frac{6 - 3}{11}

Decimal Notation

0.38799 \dots

Solution steps

\frac{3}{6 + 3}

Multiply by the conjugate

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

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

Expand

3 (6 - 3) : 18 - 33

Expand

(6 + 3) (6 - 3) : 33

= \frac{18 - 3 3}{33}

Factor out common term

3 : 3 (6 - 3)

= \frac{3 ( 6 - 3 )}{33}

Factor the number:

33 = 3 \cdot 11

= \frac{3 ( 6 - 3 )}{3 \cdot 11}

Cancel the common factor:

3

= \frac{6 - 3}{11}

- \frac{1}{x ^{2}} < 0

x^{2} + 2 x - 8 \leq 0

lo g_{2} (- 1) + lo g_{2} (- 1 - 3)

a^{3} + 8

x - 13 = 4 [3 x - 4 (x - 2)]