What is 9/(5+sqrt(2)) ?

The solution to 9/(5+sqrt(2)) is (45-9sqrt(2))/(23)

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simplify 9/(5+sqrt(2))

simplify

\frac{9}{5 + 2}

\frac{45 - 9 2}{23}

Solution steps

\frac{9}{5 + 2}

Multiply by the conjugate

\frac{5 - 2}{5 - 2}

= \frac{9 ( 5 - 2 )}{( 5 + 2 ) ( 5 - 2 )}

Expand

9 (5 - 2) : 45 - 92

Expand

(5 + 2) (5 - 2) : 23

= \frac{45 - 9 2}{23}

\frac{3}{7} \cdot \frac{14}{9}

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

(- 4 + 5 i) + (8 - 7 i)

\frac{x - 5}{5} + \frac{2 x - 1}{2}

1 6^{\frac{- 5}{4}}