化简 A/((x-1)^2)+B/(x-1)+c/(x-0.3679)

解答

化简

\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 c x + c}{( x - 1 ) ^{2} ( x - 0.3679 )}

求解步骤

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

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

的最小公倍数:

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

根据最小公倍数调整分式

= \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 )}

使用分式法则:

\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 )}

化简

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 c x + c

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

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