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

1.07179 \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

\frac{1 - sin ^{2} ( x )}{cos ( x )}

- 4 \cdot (- 9)

23 \cdot 5

\frac{56}{84}

(3 - 5 b) (3 + 5 b)