What is 4/(2-sqrt(3)) ?

The solution to 4/(2-sqrt(3)) is 8+4sqrt(3)

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simplify 4/(2-sqrt(3))

simplify

\frac{4}{2 - 3}

8 + 43

Decimal Notation

14.92820 \dots

Solution steps

\frac{4}{2 - 3}

Multiply by the conjugate

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

= \frac{4 ( 2 + 3 )}{( 2 - 3 ) ( 2 + 3 )}

Expand

4 (2 + 3) : 8 + 43

Expand

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

= \frac{8 + 4 3}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 8 + 43

38 \cdot 550

(- 4 x^{2} - x + 10) - (x^{2} + 10 x)

(x + 1) (x + 3) - (x - 2)^{2}

512 - 27 a^{9}

- \frac{8}{9}