簡約 ((1-x^2)^2)/(((1.41x)^2+(1-x^2)^2)^2)

解

簡約

\frac{( 1 - x ^{2} ) ^{2}}{( ( 1.41 x ) ^{2} + ( 1 - x ^{2} ) ^{2} ) ^{2}}

\frac{( 1 - x ^{2} ) ^{2}}{( x ^{4} - 0.0119 x ^{2} + 1 ) ^{2}}

解答ステップ

\frac{( 1 - x ^{2} ) ^{2}}{( ( 1.41 x ) ^{2} + ( 1 - x ^{2} ) ^{2} ) ^{2}}

簡素化

(1.41 x)^{2} : 1.9881 x^{2}

= \frac{( 1 - x ^{2} ) ^{2}}{( 1.9881 x ^{2} + ( 1 - x ^{2} ) ^{2} ) ^{2}}

拡張

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

= \frac{( 1 - x ^{2} ) ^{2}}{( 1.9881 x ^{2} + 1 - 2 x ^{2} + x ^{4} ) ^{2}}

条件のようなグループ

= \frac{( 1 - x ^{2} ) ^{2}}{( x ^{4} + 1.9881 x ^{2} - 2 x ^{2} + 1 ) ^{2}}

類似した元を足す:

1.9881 x^{2} - 2 x^{2} = - 0.0119 x^{2}

= \frac{( 1 - x ^{2} ) ^{2}}{( x ^{4} - 0.0119 x ^{2} + 1 ) ^{2}}