What is 2/(sqrt(7)-\sqrt{11)} ?

The solution to 2/(sqrt(7)-\sqrt{11)} is -(sqrt(7)+sqrt(11))/2

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simplify 2/(sqrt(7)-\sqrt{11)}

simplify

\frac{2}{7 - 11}

- \frac{7 + 11}{2}

Decimal Notation

- 2.98118 \dots

Solution steps

\frac{2}{7 - 11}

Multiply by the conjugate

\frac{7 + 11}{7 + 11}

= \frac{2 ( 7 + 11 )}{( 7 - 11 ) ( 7 + 11 )}

Expand

2 (7 + 11) : 27 + 211

Expand

(7 - 11) (7 + 11) : - 4

= \frac{2 7 + 2 11}{- 4}

Factor out common term

2

= \frac{2 ( 7 + 11 )}{- 4}

Factor the number:

4 = 2 \cdot 2

= \frac{2 ( 7 + 11 )}{- 2 \cdot 2}

Cancel the common factor:

2

= \frac{7 + 11}{- 2}

Apply the fraction rule:

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

= - \frac{7 + 11}{2}

2 x^{- 5}

\frac{( 3 + 4 i ) ( 1 + i )}{3 - 4 i}

7 x \cdot x

360

6 \cdot (- 12)

What is 2/(sqrt(7)-\sqrt{11)} ?
The solution to 2/(sqrt(7)-\sqrt{11)} is -(sqrt(7)+sqrt(11))/2