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

The solution to 6/(sqrt(2)+2)-6/(sqrt(2)-2) is 12

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simplify 6/(sqrt(2)+2)-6/(sqrt(2)-2)

simplify

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

12

Solution steps

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

\frac{6}{2 + 2} = - (2 - 2) \cdot 3

\frac{6}{2 - 2} = - (2 + 2) \cdot 3

= - (2 - 2) \cdot 3 - (- (2 + 2) \cdot 3)

Apply rule:

a - (- b) = a + b

- (2 - 2) \cdot 3 - (- (2 + 2) \cdot 3) = - (2 - 2) \cdot 3 + (2 + 2) \cdot 3

= - (2 - 2) \cdot 3 + (2 + 2) \cdot 3

= - 3 (2 - 2) + 3 (2 + 2)

Expand

- 3 (2 - 2) : - 32 + 6

= - 32 + 6 + 3 (2 + 2)

Expand

3 (2 + 2) : 32 + 6

= - 32 + 6 + 32 + 6

Add similar elements:

- 32 + 32 = 0

= 6 + 6

Add the numbers:

6 + 6 = 12

= 12

3 (2 x - 1)

4 (0)

(3 + 2 x)^{2}

e^{1.3}

\frac{72}{24}

What is 6/(sqrt(2)+2)-6/(sqrt(2)-2) ?
The solution to 6/(sqrt(2)+2)-6/(sqrt(2)-2) is 12