簡約 1/(1-((x^2){1-x^3}+\frac{x^3)/(1-x^2))}

解

簡約

\frac{1}{1 - ( \frac{x ^{2}}{1 - x ^{3}} + \frac{x ^{3}}{1 - x ^{2}} )}

\frac{( x - 1 ) ( x + 1 ) ( x ^{2} + x + 1 )}{x ^{5} + 2 x ^{4} + 3 x ^{3} + x ^{2} - x - 1}

解答ステップ

\frac{1}{1 - ( \frac{x ^{2}}{1 - x ^{3}} + \frac{x ^{3}}{1 - x ^{2}} )}

簡素化

1 - (\frac{x ^{2}}{1 - x ^{3}} + \frac{x ^{3}}{1 - x ^{2}}) : \frac{x ^{5} + 2 x ^{4} + 3 x ^{3} + x ^{2} - x - 1}{( x - 1 ) ( x + 1 ) ( x ^{2} + x + 1 )}

= \frac{1}{\frac{x ^{5} + 2 x ^{4} + 3 x ^{3} + x ^{2} - x - 1}{( x - 1 ) ( x + 1 ) ( x ^{2} + x + 1 )}}

分数の規則を適用する:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{( x - 1 ) ( x + 1 ) ( x ^{2} + x + 1 )}{x ^{5} + 2 x ^{4} + 3 x ^{3} + x ^{2} - x - 1}