展开 (2x^3-x+4)/((x+1)(x^2-4)^2)

解答

展开

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

\frac{2 x ^{3} - x + 4}{x ^{5} - 8 x ^{3} + 16 x + x ^{4} - 8 x ^{2} + 16}

求解步骤

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

(x^{2} - 4)^{2} = x^{4} - 8 x^{2} + 16

= \frac{2 x ^{3} - x + 4}{( x + 1 ) ( x ^{4} - 8 x ^{2} + 16 )}

乘开

(x + 1) (x^{4} - 8 x^{2} + 16) : x^{5} - 8 x^{3} + 16 x + x^{4} - 8 x^{2} + 16

= \frac{2 x ^{3} - x + 4}{x ^{5} - 8 x ^{3} + 16 x + x ^{4} - 8 x ^{2} + 16}

e x p an d (5 x^{3} - 3)^{5} 4 - 4 x^{5} - 3

e x p an d A (3, 2, - 4) B (- 5, 4, 4)

e x p an d \frac{4 s ^{2} + 36 + s ^{3} + 16 s}{( s ^{2} + 9 ) ( s ^{2} + 16 )}

e x p an d \frac{1}{3 \cdot x ( x - 8 )}

e x p an d \frac{1}{5} (15 + 10 x - 5)