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

The solution to 2/(4-sqrt(5)) is (8+2sqrt(5))/(11)

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simplify 2/(4-sqrt(5))

simplify

\frac{2}{4 - 5}

\frac{8 + 2 5}{11}

Decimal Notation

1.13383 \dots

Solution steps

\frac{2}{4 - 5}

Multiply by the conjugate

\frac{4 + 5}{4 + 5}

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

Expand

2 (4 + 5) : 8 + 25

Expand

(4 - 5) (4 + 5) : 11

= \frac{8 + 2 5}{11}

36 x^{4} - 48 x^{6} - 72 x^{3} + 60 x^{5}

lo g_{10} (\frac{5}{3})

3 - 33 i

(2 x - 3 y^{4} z^{2})^{4}

\frac{x ^{2} - 25}{x ^{2} - 4 x - 5}