展开 (x^2-x+1)/((1-x)^2(1-3x))

解答

展开

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

\frac{x ^{2} - x + 1}{1 - 5 x + 7 x ^{2} - 3 x ^{3}}

求解步骤

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

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

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

乘开

(1 - 2 x + x^{2}) (1 - 3 x) : 1 - 5 x + 7 x^{2} - 3 x^{3}

= \frac{x ^{2} - x + 1}{1 - 5 x + 7 x ^{2} - 3 x ^{3}}

e x p an d cos (2 (t - 1))

e x p an d \frac{x ( x - 5 )}{( x + 3 ) ( x - 1 )}

e x p an d \frac{9 x ^{2} ( x - 7 ) ^{2}}{( x + 5 ) ^{2}}

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

e x p an d e^{7 t} (27 \cdot U (t - 18))