展开 ((x-a)(x-b)(x-a-d))/((x-c)(x-d)(x-a-b))

解答

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

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

求解步骤

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

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

= \frac{( x - a ) ( x - b ) ( x - a - d )}{x ^{3} - a x ^{2} - b x ^{2} - d x ^{2} + a d x + b d x - c x ^{2} + a c x + b c x + d c x - a d c - b d c}

乘开

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

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

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