What is 4/(5-2sqrt(3)) ?

The solution to 4/(5-2sqrt(3)) is (20+8sqrt(3))/(13)

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simplify 4/(5-2sqrt(3))

simplify

\frac{4}{5 - 2 3}

\frac{20 + 8 3}{13}

Decimal Notation

2.60433 \dots

Solution steps

\frac{4}{5 - 2 3}

Multiply by the conjugate

\frac{5 + 2 3}{5 + 2 3}

= \frac{4 ( 5 + 2 3 )}{( 5 - 2 3 ) ( 5 + 2 3 )}

Expand

4 (5 + 23) : 20 + 83

Expand

(5 - 23) (5 + 23) : 13

= \frac{20 + 8 3}{13}

- (3 + h)^{2}

16 m^{5} - 81 m^{3}

(9 + i) - (8 + 3 i)

(8 + 2 i) + (3 + 9 i)

\frac{- 54}{- 6}