What is 2/(2+sqrt(6)) ?

The solution to 2/(2+sqrt(6)) is -2+sqrt(6)

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simplify 2/(2+sqrt(6))

simplify

\frac{2}{2 + 6}

- 2 + 6

Decimal Notation

0.44948 \dots

Solution steps

\frac{2}{2 + 6}

Multiply by the conjugate

\frac{2 - 6}{2 - 6}

= \frac{2 ( 2 - 6 )}{( 2 + 6 ) ( 2 - 6 )}

Expand

2 (2 - 6) : 4 - 26

Expand

(2 + 6) (2 - 6) : - 2

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

Factor out common term

2 : 2 (2 - 6)

= \frac{2 ( 2 - 6 )}{- 2}

Cancel the common factor:

2

= \frac{2 - 6}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (2 - 6)

- (2 - 6) = - 2 + 6

= - 2 + 6

(x + y + 3) (x + y - 2)

5 x^{2} - 25 x

(2 x^{3} + 5 x)^{2}

(4 + x - 2) (4 + x + 2)

- 2 y^{3} - y^{2} + y^{2} + y^{3}