展开 ((x^3+x^2+21))/(x(2x-5)^3(x^2+2x+5)^2)

解答

展开

\frac{( x ^{3} + x ^{2} + 21 )}{x ( 2 x - 5 ) ^{3} ( x ^{2} + 2 x + 5 ) ^{2}}

\frac{x ^{3} + x ^{2} + 21}{8 x ^{8} - 28 x ^{7} + 22 x ^{6} - 205 x ^{5} + 600 x ^{4} - 250 x ^{3} + 1250 x ^{2} - 3125 x}

求解步骤

\frac{x ^{3} + x ^{2} + 21}{x ( 2 x - 5 ) ^{3} ( x ^{2} + 2 x + 5 ) ^{2}}

(2 x - 5)^{3} = 8 x^{3} - 60 x^{2} + 150 x - 125

= \frac{x ^{3} + x ^{2} + 21}{x ( 8 x ^{3} - 60 x ^{2} + 150 x - 125 ) ( x ^{2} + 2 x + 5 ) ^{2}}

(x^{2} + 2 x + 5)^{2} = x^{4} + 4 x^{3} + 14 x^{2} + 20 x + 25

= \frac{x ^{3} + x ^{2} + 21}{x ( 8 x ^{3} - 60 x ^{2} + 150 x - 125 ) ( x ^{4} + 4 x ^{3} + 14 x ^{2} + 20 x + 25 )}

乘开

x (8 x^{3} - 60 x^{2} + 150 x - 125) (x^{4} + 4 x^{3} + 14 x^{2} + 20 x + 25) : 8 x^{8} - 28 x^{7} + 22 x^{6} - 205 x^{5} + 600 x^{4} - 250 x^{3} + 1250 x^{2} - 3125 x

= \frac{x ^{3} + x ^{2} + 21}{8 x ^{8} - 28 x ^{7} + 22 x ^{6} - 205 x ^{5} + 600 x ^{4} - 250 x ^{3} + 1250 x ^{2} - 3125 x}

e x p an d 3 (x + 3) (x - 3) (x - 5) (x + 1) + 3

e x p an d (f (x) + g (x)) x^{'}

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

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

cos (\frac{π}{2} + π)