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

The solution to (sqrt(3)+2)/(1-sqrt(3)) is -(3sqrt(3)+5)/2

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simplify (sqrt(3)+2)/(1-sqrt(3))

simplify

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

- \frac{3 3 + 5}{2}

Decimal Notation

- 5.09807 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(3 + 2) (1 + 3) : 33 + 5

Expand

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

= \frac{3 3 + 5}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{3 3 + 5}{2}

\frac{3 a}{8} - 2 = \frac{2 a + 9}{5}

- 4 x^{2} + 4 x - 1

x^{2} + \frac{3}{2} x + \frac{1}{2} = 0

x^{2} + x = 1.5 x^{2}

- 2 \geq - 10

What is (sqrt(3)+2)/(1-sqrt(3)) ?
The solution to (sqrt(3)+2)/(1-sqrt(3)) is -(3sqrt(3)+5)/2