簡約 A/((x-1)^2)+B/(x-1)+C/(x-0.3679)

解

簡約

\frac{A}{( x - 1 ) ^{2}} + \frac{B}{x - 1} + \frac{C}{x - 0.3679}

\frac{A x - 0.3679 A + x ^{2} B - 1.3679 B x + 0.3679 B + x ^{2} C - 2 x C + C}{( x - 1 ) ^{2} ( x - 0.3679 )}

解答ステップ

\frac{A}{( x - 1 ) ^{2}} + \frac{B}{x - 1} + \frac{C}{x - 0.3679}

以下の最小公倍数:

(x - 1)^{2}, x - 1, x - 0.3679 : (x - 1)^{2} (x - 0.3679)

LCMに基づいて分数を調整する

= \frac{A ( x - 0.3679 )}{( x - 1 ) ^{2} ( x - 0.3679 )} + \frac{B ( x - 1 ) ( x - 0.3679 )}{( x - 1 ) ^{2} ( x - 0.3679 )} + \frac{C ( x - 1 ) ^{2}}{( x - 1 ) ^{2} ( x - 0.3679 )}

分数の規則を適用する:

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

= \frac{A ( x - 0.3679 ) + B ( x - 1 ) ( x - 0.3679 ) + C ( x - 1 ) ^{2}}{( x - 1 ) ^{2} ( x - 0.3679 )}

簡素化

A (x - 0.3679) + B (x - 1) (x - 0.3679) + C (x - 1)^{2} : A x - 0.3679 A + x^{2} B - 1.3679 B x + 0.3679 B + x^{2} C - 2 x C + C

= \frac{A x - 0.3679 A + x ^{2} B - 1.3679 B x + 0.3679 B + x ^{2} C - 2 x C + C}{( x - 1 ) ^{2} ( x - 0.3679 )}