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

The solution to 4/(4-sqrt(5)) is (16+4sqrt(5))/(11)

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simplify 4/(4-sqrt(5))

simplify

\frac{4}{4 - 5}

\frac{16 + 4 5}{11}

Decimal Notation

2.26766 \dots

Solution steps

\frac{4}{4 - 5}

Multiply by the conjugate

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

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

Expand

4 (4 + 5) : 16 + 45

Expand

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

= \frac{16 + 4 5}{11}

lo g_{\frac{1}{6}} (6)

73

\frac{5 π}{2} - 2 π

\frac{3}{s ^{2} + 9} + 1

\frac{e ^{- 6} \cdot 6 ^{0}}{0 !}