What is (sqrt(2)-sqrt(10))/(sqrt(2)+\sqrt{10)} ?

The solution to (sqrt(2)-sqrt(10))/(sqrt(2)+\sqrt{10)} is -(3-sqrt(5))/2

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simplify (sqrt(2)-sqrt(10))/(sqrt(2)+\sqrt{10)}

simplify

\frac{2 - 10}{2 + 10}

- \frac{3 - 5}{2}

Decimal Notation

- 0.38196 \dots

Solution steps

\frac{2 - 10}{2 + 10}

Multiply by the conjugate

\frac{2 - 10}{2 - 10}

= \frac{( 2 - 10 ) ( 2 - 10 )}{( 2 + 10 ) ( 2 - 10 )}

Expand

(2 - 10) (2 - 10) : 12 - 45

Expand

(2 + 10) (2 - 10) : - 8

= \frac{12 - 4 5}{- 8}

Factor out common term

4 : 4 (3 - 5)

= \frac{4 ( 3 - 5 )}{- 8}

Factor the number:

8 = 4 \cdot 2

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

Cancel the common factor:

4

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

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

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

4^{2} - 5 x - 6

3 + (- 1)

\frac{1}{6} \cdot 27

6 x^{2} - 5 x - 25

\frac{21 + { 361 }}{2}

What is (sqrt(2)-sqrt(10))/(sqrt(2)+\sqrt{10)} ?
The solution to (sqrt(2)-sqrt(10))/(sqrt(2)+\sqrt{10)} is -(3-sqrt(5))/2