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

The solution to 3/(4-sqrt(5)) is (12+3sqrt(5))/(11)

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simplify 3/(4-sqrt(5))

simplify

\frac{3}{4 - 5}

\frac{12 + 3 5}{11}

Decimal Notation

1.70074 \dots

Solution steps

\frac{3}{4 - 5}

Multiply by the conjugate

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

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

Expand

3 (4 + 5) : 12 + 35

Expand

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

= \frac{12 + 3 5}{11}

\frac{2}{7} \div \frac{1}{8}

- \frac{3}{8} + (- \frac{9}{10})

\frac{( - 3 i ) ^{2} ( 1 - 2 i )}{2 + 2 i}

10 (m + 4 n)

- 10 - (- 7)