因数 (1+1/x)^2-(1-1/x)^2

解

因数

(1 + \frac{1}{x})^{2} - (1 - \frac{1}{x})^{2}

2 \cdot \frac{2}{x}

解答ステップ

(1 + \frac{1}{x})^{2} - (1 - \frac{1}{x})^{2}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

(1 + \frac{1}{x})^{2} - (1 - \frac{1}{x})^{2} = ((1 + \frac{1}{x}) + (1 - \frac{1}{x})) ((1 + \frac{1}{x}) - (1 - \frac{1}{x}))

= ((1 + \frac{1}{x}) + (1 - \frac{1}{x})) ((1 + \frac{1}{x}) - (1 - \frac{1}{x}))

簡素化

((1 + \frac{1}{x}) + (1 - \frac{1}{x})) ((1 + \frac{1}{x}) - (1 - \frac{1}{x})) : 2 \cdot \frac{2}{x}

= 2 \cdot \frac{2}{x}