What is 2/(sqrt(3)+\sqrt{7)} ?

The solution to 2/(sqrt(3)+\sqrt{7)} is -(sqrt(3)-sqrt(7))/2

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simplify 2/(sqrt(3)+\sqrt{7)}

simplify

\frac{2}{3 + 7}

- \frac{3 - 7}{2}

Solution steps

\frac{2}{3 + 7}

Multiply by the conjugate

\frac{3 - 7}{3 - 7}

= \frac{2 ( 3 - 7 )}{( 3 + 7 ) ( 3 - 7 )}

Expand

2 (3 - 7) : 23 - 27

Expand

(3 + 7) (3 - 7) : - 4

= \frac{2 3 - 2 7}{- 4}

Factor out common term

2

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

Factor the number:

4 = 2 \cdot 2

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

Cancel the common factor:

2

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

Apply the fraction rule:

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

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

(1 - x) + 5 c (1 - x)

5 (7)

\frac{u ^{\frac{1}{2}}}{\frac{1}{2}}

5 (2 v) + 6 v

What is 2/(sqrt(3)+\sqrt{7)} ?
The solution to 2/(sqrt(3)+\sqrt{7)} is -(sqrt(3)-sqrt(7))/2