What is 4/(3-sqrt(3)) ?

The solution to 4/(3-sqrt(3)) is (2(3+sqrt(3)))/3

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simplify 4/(3-sqrt(3))

simplify

\frac{4}{3 - 3}

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

Decimal Notation

3.15470 \dots

Solution steps

\frac{4}{3 - 3}

Multiply by the conjugate

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

= \frac{4 ( 3 + 3 )}{( 3 - 3 ) ( 3 + 3 )}

Expand

4 (3 + 3) : 12 + 43

Expand

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

= \frac{12 + 4 3}{6}

Factor out common term

4 : 4 (3 + 3)

= \frac{4 ( 3 + 3 )}{6}

Factor the number:

4 = 2 \cdot 2

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

Factor the number:

6 = 2 \cdot 3

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

Cancel the common factor:

2

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

(x^{2})^{n + 1}

\frac{3}{x - 1} + \frac{x}{x + 2}

\frac{- 3}{3}

\frac{( 4 t ^{5} ) ^{3}}{2 t ^{3}}