簡約 algebra(1-3x+2x^2)/((x^2+1)(x^2-1))

解

簡約

a l g e b r a \frac{1 - 3 x + 2 x ^{2}}{( x ^{2} + 1 ) ( x ^{2} - 1 )}

\frac{e a ^{2} l b g r ( 2 x - 1 )}{( x + 1 ) ( x ^{2} + 1 )}

解答ステップ

a l g e b r a \frac{1 - 3 x + 2 x ^{2}}{( x ^{2} + 1 ) ( x ^{2} - 1 )}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

aa = a^{1 + 1}

= l g e b r a^{1 + 1} \frac{1 - 3 x + 2 x ^{2}}{( x ^{2} + 1 ) ( x ^{2} - 1 )}

数を足す:

1 + 1 = 2

= l g e b r a^{2} \frac{1 - 3 x + 2 x ^{2}}{( x ^{2} + 1 ) ( x ^{2} - 1 )}

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

= e a^{2} l b g r \frac{2 x - 1}{( x + 1 ) ( x ^{2} + 1 )}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 2 x - 1 ) l g e b r a ^{2}}{( x + 1 ) ( x ^{2} + 1 )}