What is 6/(3-sqrt(5)) ?

The solution to 6/(3-sqrt(5)) is (3(3+sqrt(5)))/2

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simplify 6/(3-sqrt(5))

simplify

\frac{6}{3 - 5}

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

Decimal Notation

7.85410 \dots

Solution steps

\frac{6}{3 - 5}

Multiply by the conjugate

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

= \frac{6 ( 3 + 5 )}{( 3 - 5 ) ( 3 + 5 )}

Expand

6 (3 + 5) : 18 + 65

Expand

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

= \frac{18 + 6 5}{4}

Factor out common term

6 : 6 (3 + 5)

= \frac{6 ( 3 + 5 )}{4}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 3 ( 3 + 5 )}{4}

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

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

x^{3} + x^{2} - 30 x

\frac{R}{R + s L + \frac{1}{s C} + A}

\frac{77}{7}

(21 + 56) (7 - 1)