簡約 (1+1/x)^2-(1-1/x)^2

解

簡約

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

\frac{4}{x}

解答ステップ

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

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

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

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

結合

\frac{( x + 1 ) ^{2}}{x ^{2}} - \frac{( x - 1 ) ^{2}}{x ^{2}} : \frac{4}{x}

= \frac{4}{x}