因式分解 (1+1/x)^2-(1-1/x)^2

解答

因式分解

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

2 \cdot \frac{2}{x}

求解步骤

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

使用平方差公式:

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}))

化简

((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}

f a c t or 14 a^{4} b^{2} - 21 a^{3} b^{2}

f a c t or r^{2} + 85 rs + 84 s^{2}

\frac{2 x - 4}{5} = 4

s im pl i f y lo g_{e} (2)

s im pl i f y 32 x^{6} y^{3}