展開する (xdv(4+v^2))/((4-v^2)(1+x^2))

解

展開する

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

\frac{4 x d v + x v ^{2} d v}{4 + 4 x ^{2} - v ^{2} - x ^{2} v ^{2}}

解答ステップ

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

拡張

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

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

拡張

x d v (4 + v^{2}) : 4 x d v + x v^{2} d v

= \frac{4 x d v + x v ^{2} d v}{4 + 4 x ^{2} - v ^{2} - x ^{2} v ^{2}}