展开 (3x^2+5x-9)/(x^3(x^2+2)^2)

解答

展开

\frac{3 x ^{2} + 5 x - 9}{x ^{3} ( x ^{2} + 2 ) ^{2}}

\frac{3 x ^{2} + 5 x - 9}{x ^{7} + 4 x ^{5} + 4 x ^{3}}

求解步骤

\frac{3 x ^{2} + 5 x - 9}{x ^{3} ( x ^{2} + 2 ) ^{2}}

(x^{2} + 2)^{2} = x^{4} + 4 x^{2} + 4

= \frac{3 x ^{2} + 5 x - 9}{x ^{3} ( x ^{4} + 4 x ^{2} + 4 )}

乘开

x^{3} (x^{4} + 4 x^{2} + 4) : x^{7} + 4 x^{5} + 4 x^{3}

= \frac{3 x ^{2} + 5 x - 9}{x ^{7} + 4 x ^{5} + 4 x ^{3}}

e x p an d (e^{x} - 1)^{3}

e x p an d cos (x) (tan (x) + sec (x))

s im pl i f y (- 1 + \frac{4 i}{n})^{3}

e x p an d \frac{2 s - 4}{( s ^{2} + s ) ( s ^{2} + 1 )}

e x p an d (2 sin (x) - 1) (sin (x) + 2)