What is 3/(3-2sqrt(3)) ?

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

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simplify 3/(3-2sqrt(3))

simplify

\frac{3}{3 - 2 3}

- 3 - 23

Decimal Notation

- 6.46410 \dots

Solution steps

\frac{3}{3 - 2 3}

Multiply by the conjugate

\frac{3 + 2 3}{3 + 2 3}

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

Expand

3 (3 + 23) : 9 + 63

Expand

(3 - 23) (3 + 23) : - 3

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

Factor out common term

3 : 3 (3 + 23)

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

Cancel the common factor:

3

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

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (3 + 23)

- (3 + 23) = - 3 - 23

= - 3 - 23

x^{2} + x + \frac{1}{2}

21 x^{2} - 22 x - 8

11 + 11

x^{2} - x^{3} y^{5}