What is 2/(sqrt(14)-2) ?

The solution to 2/(sqrt(14)-2) is (sqrt(14)+2)/5

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simplify 2/(sqrt(14)-2)

simplify

\frac{2}{14 - 2}

\frac{14 + 2}{5}

Decimal Notation

1.14833 \dots

Solution steps

\frac{2}{14 - 2}

Multiply by the conjugate

\frac{14 + 2}{14 + 2}

= \frac{2 ( 14 + 2 )}{( 14 - 2 ) ( 14 + 2 )}

Expand

2 (14 + 2) : 214 + 4

Expand

(14 - 2) (14 + 2) : 10

= \frac{2 14 + 4}{10}

Factor out common term

2 : 2 (14 + 2)

= \frac{2 ( 14 + 2 )}{10}

Factor the number:

10 = 2 \cdot 5

= \frac{2 ( 14 + 2 )}{2 \cdot 5}

Cancel the common factor:

2

= \frac{14 + 2}{5}

\frac{36}{- 6}

2 lo g_{5} (100) - 4 lo g_{5} (50)

(- 5 g) (x)

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

\frac{cos ( a )}{1 + cot ^{2} ( a )}