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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3/(3-sqrt(3))

simplify

\frac{3}{3 - 3}

\frac{3 + 3}{2}

Decimal Notation

2.36602 \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}

(2)^{- 3}

\frac{5}{x + 8} < 0

6 y^{2} + 30 y = 0

a^{2} + 14 a + 48

v^{2} + 2 v - 8 = 0