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

The solution to 3/(4+4sqrt(5)) is -(3(1-sqrt(5)))/(16)

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simplify 3/(4+4sqrt(5))

simplify

\frac{3}{4 + 4 5}

- \frac{3 ( 1 - 5 )}{16}

Decimal Notation

0.23176 \dots

Solution steps

\frac{3}{4 + 4 5}

Multiply by the conjugate

\frac{4 - 4 5}{4 - 4 5}

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

Expand

3 (4 - 45) : 12 - 125

Expand

(4 + 45) (4 - 45) : - 64

= \frac{12 - 12 5}{- 64}

Factor out common term

12 : 12 (1 - 5)

= \frac{12 ( 1 - 5 )}{- 64}

Factor the number:

12 = 4 \cdot 3

= \frac{4 \cdot 3 ( 1 - 5 )}{- 64}

Factor the number:

64 = 4 \cdot 16

= \frac{4 \cdot 3 ( 1 - 5 )}{- 4 \cdot 16}

Cancel the common factor:

4

= \frac{3 ( 1 - 5 )}{- 16}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{3 ( 1 - 5 )}{16}

x - 4 \leq 3

\frac{14}{3} - 1

- 2 s - 7 \leq 5

\frac{1}{9} \cdot 2

(\frac{5}{9})^{1}