展开 1/((x+1)^2(x-2)^3)

解答

展开

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

\frac{1}{x ^{5} - 4 x ^{4} + x ^{3} + 10 x ^{2} - 4 x - 8}

求解步骤

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

(x - 2)^{3} = x^{3} - 6 x^{2} + 12 x - 8

= \frac{1}{( x ^{2} + 2 x + 1 ) ( x ^{3} - 6 x ^{2} + 12 x - 8 )}

乘开

(x^{2} + 2 x + 1) (x^{3} - 6 x^{2} + 12 x - 8) : x^{5} - 4 x^{4} + x^{3} + 10 x^{2} - 4 x - 8

= \frac{1}{x ^{5} - 4 x ^{4} + x ^{3} + 10 x ^{2} - 4 x - 8}

e x p an d (x + y = 2,) (x^{(2)} + y^{(2)} = 4)

e x p an d - e^{t} \cdot (2 e^{t} + 8 t e^{t})

e x p an d x y d y (y + 1) (1 - x) d x

e x p an d y (2 x^{2} - x y + y^{2}) d x

e x p an d \frac{1}{2 ( 4 x - 10 ) ( 2 x + 3 )}