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

The solution to (3-sqrt(5))/(3+sqrt(5)) is (7-3sqrt(5))/2

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

simplify

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

\frac{7 - 3 5}{2}

Solution steps

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

Multiply by the conjugate

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

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

Expand

(3 - 5) (3 - 5) : 14 - 65

Expand

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

= \frac{14 - 6 5}{4}

Factor out common term

2 : 2 (7 - 35)

= \frac{2 ( 7 - 3 5 )}{4}

Factor the number:

4 = 2 \cdot 2

= \frac{2 ( 7 - 3 5 )}{2 \cdot 2}

Cancel the common factor:

2

= \frac{7 - 3 5}{2}

(- 4 + 5 i) + (8 - 7 i)

\frac{x - 5}{5} + \frac{2 x - 1}{2}

1 6^{\frac{- 5}{4}}

(a^{2} b^{4})^{2}

(1 - 3)^{3}

What is (3-sqrt(5))/(3+sqrt(5)) ?
The solution to (3-sqrt(5))/(3+sqrt(5)) is (7-3sqrt(5))/2