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

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

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simplify 2/(3-sqrt(5))

simplify

\frac{2}{3 - 5}

\frac{3 + 5}{2}

Decimal Notation

2.61803 \dots

Solution steps

\frac{2}{3 - 5}

Multiply by the conjugate

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

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

Expand

2 (3 + 5) : 6 + 25

Expand

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

= \frac{6 + 2 5}{4}

Factor out common term

2 : 2 (3 + 5)

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

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

= \frac{3 + 5}{2}

4 z - 7 \leq - 7 z + 9

lo g_{3} (\frac{1}{81})

(\frac{2 x}{3 y})^{5}

\frac{- 2 + 3 i}{4 + 2 i}

2 + 3 f > 8