What is expand (sqrt(2)(2-sqrt(3))+10)/4 ?

The solution to expand (sqrt(2)(2-sqrt(3))+10)/4 is 1/(sqrt(2))-(sqrt(3))/(2sqrt(2))+5/2

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expand (sqrt(2)(2-sqrt(3))+10)/4

expand

\frac{2 ( 2 - 3 ) + 10}{4}

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

Decimal Notation

2.59473 \dots

Solution steps

\frac{2 ( 2 - 3 ) + 10}{4}

Expand

2 (2 - 3) + 10 : 22 - 6 + 10

= \frac{2 2 - 6 + 10}{4}

Apply the fraction rule:

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

\frac{2 2 - 6 + 10}{4} = \frac{2 2}{4} - \frac{6}{4} + \frac{10}{4}

= \frac{2 2}{4} - \frac{6}{4} + \frac{10}{4}

Cancel

\frac{2 2}{4} : \frac{1}{2}

= \frac{1}{2} - \frac{6}{4} + \frac{10}{4}

Cancel

\frac{6}{4} : \frac{3}{2 2}

= \frac{1}{2} - \frac{3}{2 2} + \frac{10}{4}

Cancel

\frac{10}{4} : \frac{5}{2}

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

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What is expand (sqrt(2)(2-sqrt(3))+10)/4 ?
The solution to expand (sqrt(2)(2-sqrt(3))+10)/4 is 1/(sqrt(2))-(sqrt(3))/(2sqrt(2))+5/2