簡約 6/(sqrt(2)+2)-6/(sqrt(2)-2)

解

簡約

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

12

解答ステップ

\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)

規則を適用する:

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)

拡張

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

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

拡張

3 (2 + 2) : 32 + 6

= - 32 + 6 + 32 + 6

類似した元を足す:

- 32 + 32 = 0

= 6 + 6

数を足す:

6 + 6 = 12

= 12