What is (1+sqrt(3))/(sqrt(3)-1) ?

The solution to (1+sqrt(3))/(sqrt(3)-1) is 2+sqrt(3)

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simplify (1+sqrt(3))/(sqrt(3)-1)

simplify

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

2 + 3

Solution steps

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

Multiply by the conjugate

\frac{3 + 1}{3 + 1}

= \frac{( 1 + 3 ) ( 3 + 1 )}{( 3 - 1 ) ( 3 + 1 )}

Expand

(1 + 3) (3 + 1) : 4 + 23

Expand

(3 - 1) (3 + 1) : 2

= \frac{4 + 2 3}{2}

Factor out common term

2 : 2 (2 + 3)

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

Cancel the common factor:

2

= 2 + 3

20 \cdot 9

(3 x + 4) (x^{2} - 4 x + 5)

(x + 6) (x + 4) (x + 3)

\frac{1}{6} \div \frac{2}{3}

(- 3)^{2} + (4)^{2}

What is (1+sqrt(3))/(sqrt(3)-1) ?
The solution to (1+sqrt(3))/(sqrt(3)-1) is 2+sqrt(3)