What is (2sqrt(5))/(3+sqrt(5)) ?

The solution to (2sqrt(5))/(3+sqrt(5)) is (3sqrt(5)-5)/2

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simplify (2sqrt(5))/(3+sqrt(5))

simplify

\frac{2 5}{3 + 5}

\frac{3 5 - 5}{2}

Decimal Notation

0.85410 \dots

Solution steps

\frac{2 5}{3 + 5}

Multiply by the conjugate

\frac{3 - 5}{3 - 5}

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

Expand

2 (3 - 5) : 6 - 25

Expand

(3 + 5) (3 - 5) : 4

= \frac{( 6 - 2 5 ) 5}{4}

Factor out common term

2 : 2 (3 - 5)

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

Factor the number:

4 = 2 \cdot 2

= \frac{2 ( 3 - 5 ) 5}{2 \cdot 2}

Cancel the common factor:

2

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

(3 - 5) 5 = 35 - 5

= \frac{3 5 - 5}{2}

5 \cdot \frac{2}{2}

3 - x - (2 x - 4)

- 5 + (- 12)

\frac{5}{4} + \frac{3}{5}

(- 2 x^{2} - 2 x - 7) - (2 x^{2} + 7)

What is (2sqrt(5))/(3+sqrt(5)) ?
The solution to (2sqrt(5))/(3+sqrt(5)) is (3sqrt(5)-5)/2