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

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

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simplify 6/(3-sqrt(3))

simplify

\frac{6}{3 - 3}

3 + 3

Decimal Notation

4.73205 \dots

Solution steps

\frac{6}{3 - 3}

Multiply by the conjugate

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

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

Expand

6 (3 + 3) : 18 + 63

Expand

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

= \frac{18 + 6 3}{6}

Factor out common term

6 : 6 (3 + 3)

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

Cancel the common factor:

6

= 3 + 3

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

(x - 1) (y - 1)

x^{3} + 13 x^{2} + 40 x + 36

43 \cdot 26

\frac{0}{13}