What is expand ((2+sqrt(3))(sqrt(5)-1))/2 ?

The solution to expand ((2+sqrt(3))(sqrt(5)-1))/2 is -(sqrt(3))/2+(sqrt(15))/2+sqrt(5)-1

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expand ((2+sqrt(3))(sqrt(5)-1))/2

expand

\frac{( 2 + 3 ) ( 5 - 1 )}{2}

- \frac{3}{2} + \frac{15}{2} + 5 - 1

Decimal Notation

2.30653 \dots

Solution steps

\frac{( 2 + 3 ) ( 5 - 1 )}{2}

Expand

(2 + 3) (5 - 1) : 25 - 2 + 15 - 3

= \frac{2 5 - 2 + 15 - 3}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 5 - 2 + 15 - 3}{2} = \frac{2 5}{2} - \frac{2}{2} + \frac{15}{2} - \frac{3}{2}

= \frac{2 5}{2} - \frac{2}{2} + \frac{15}{2} - \frac{3}{2}

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

= \frac{2 5}{2} - 1 + \frac{15}{2} - \frac{3}{2}

Group like terms

= - \frac{3}{2} + \frac{2 5}{2} + \frac{15}{2} - 1

Divide the numbers:

\frac{2}{2} = 1

= - \frac{3}{2} + 5 + \frac{15}{2} - 1

Group like terms

= - \frac{3}{2} + \frac{15}{2} + 5 - 1

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\frac{7 x ^{2} - 14 x + 21}{( x - 2 ) ( x ^{2} + 3 )}

What is expand ((2+sqrt(3))(sqrt(5)-1))/2 ?
The solution to expand ((2+sqrt(3))(sqrt(5)-1))/2 is -(sqrt(3))/2+(sqrt(15))/2+sqrt(5)-1