簡約 4x^2-1+2/((x^2-x-2))-3/((x^2-3x+2))

解

簡約

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

\frac{4 x ^{5} - 8 x ^{4} - 5 x ^{3} + 10 x ^{2} - 7}{( x + 1 ) ( x - 2 ) ( x - 1 )}

解答ステップ

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

結合

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

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

4 x^{2}

を分数に変換する

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

1

を分数に変換する

: \frac{( x + 1 ) ( x - 2 ) ( x - 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )}

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

分数の規則を適用する:

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

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

簡素化

4 x^{2} (x + 1) (x - 2) (x - 1) - (x + 1) (x - 2) (x - 1) + 2 (x - 1) - 3 (x + 1) : 4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} - 7

= \frac{4 x ^{5} - 8 x ^{4} - 5 x ^{3} + 10 x ^{2} - 7}{( x + 1 ) ( x - 2 ) ( x - 1 )}