What is 3/(4+sqrt(3)) ?

The solution to 3/(4+sqrt(3)) is (12-3sqrt(3))/(13)

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simplify 3/(4+sqrt(3))

simplify

\frac{3}{4 + 3}

\frac{12 - 3 3}{13}

Decimal Notation

0.52337 \dots

Solution steps

\frac{3}{4 + 3}

Multiply by the conjugate

\frac{4 - 3}{4 - 3}

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

Expand

3 (4 - 3) : 12 - 33

Expand

(4 + 3) (4 - 3) : 13

= \frac{12 - 3 3}{13}

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