簡約 ((x^2+1)/((x^2)))^2-((x^2-1)/((x^2)))^2

解

簡約

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

\frac{4}{x ^{2}}

解答ステップ

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

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

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

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

結合

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

= \frac{4}{x ^{2}}