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

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

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simplify (3+sqrt(3))/(3-sqrt(3))

simplify

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

2 + 3

Decimal Notation

3.73205 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(3 + 3) (3 + 3) : 12 + 63

Expand

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

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

Factor out common term

6 : 6 (2 + 3)

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

Cancel the common factor:

6

= 2 + 3

3 (3 x - 3)^{2} + 11 = 41

- 11 s^{2} + 26 s + 61 = 0

(12 mn) (- m^{3} n^{- 2} p^{5}) (2 m)

3 (2 y - 3) = 7

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

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