展开 1/((x-a)(x-b)(x-c))

解答

展开

\frac{1}{( x - a ) ( x - b ) ( x - c )}

\frac{1}{x ^{3} - c x ^{2} - b x ^{2} + b c x - a x ^{2} + a c x + ab x - ab c}

求解步骤

\frac{1}{( x - a ) ( x - b ) ( x - c )}

乘开

(x - a) (x - b) (x - c) : x^{3} - c x^{2} - b x^{2} + b c x - a x^{2} + a c x + ab x - ab c

= \frac{1}{x ^{3} - c x ^{2} - b x ^{2} + b c x - a x ^{2} + a c x + ab x - ab c}

e x p an d 4 x 3 - 7 + 10 x

s im pl i f y (7 x - \frac{1}{2}) (7 x + \frac{1}{2})

e x p an d \frac{y ^{2} ( 1 - x ^{2} )}{2}

e x p an d \frac{x ( x - 1 )}{x ^{2} + 2 x + 1}

e x p an d 4 (3 e - 5)