展開する (4s(8+4s+s^2))/((2+s)^2(4+s))

解

展開する

\frac{4 s ( 8 + 4 s + s ^{2} )}{( 2 + s ) ^{2} ( 4 + s )}

\frac{32 s + 16 s ^{2} + 4 s ^{3}}{16 + 20 s + 8 s ^{2} + s ^{3}}

解答ステップ

\frac{4 s ( 8 + 4 s + s ^{2} )}{( 2 + s ) ^{2} ( 4 + s )}

(2 + s)^{2} = 4 + 4 s + s^{2}

= \frac{4 s ( s ^{2} + 4 s + 8 )}{( s ^{2} + 4 s + 4 ) ( s + 4 )}

拡張

(4 + 4 s + s^{2}) (4 + s) : 16 + 20 s + 8 s^{2} + s^{3}

= \frac{4 s ( s ^{2} + 4 s + 8 )}{16 + 20 s + 8 s ^{2} + s ^{3}}

拡張

4 s (8 + 4 s + s^{2}) : 32 s + 16 s^{2} + 4 s^{3}

= \frac{32 s + 16 s ^{2} + 4 s ^{3}}{16 + 20 s + 8 s ^{2} + s ^{3}}