What is 3/(6+sqrt(5)) ?

The solution to 3/(6+sqrt(5)) is (18-3sqrt(5))/(31)

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simplify 3/(6+sqrt(5))

simplify

\frac{3}{6 + 5}

\frac{18 - 3 5}{31}

Decimal Notation

0.36425 \dots

Solution steps

\frac{3}{6 + 5}

Multiply by the conjugate

\frac{6 - 5}{6 - 5}

= \frac{3 ( 6 - 5 )}{( 6 + 5 ) ( 6 - 5 )}

Expand

3 (6 - 5) : 18 - 35

Expand

(6 + 5) (6 - 5) : 31

= \frac{18 - 3 5}{31}

\frac{69}{4}

\frac{4 x}{x ^{2} - 4} + \frac{x}{x + 2}

(\frac{1}{8} a - \frac{3}{4} b)^{2}

\frac{2}{3} \div \frac{1}{9}

\frac{7}{9} + \frac{1}{15}