展开 (x+1)/((x+2)^3(x+5)(x+6)^2)

解答

展开

\frac{x + 1}{( x + 2 ) ^{3} \cdot ( x + 5 ) \cdot ( x + 6 ) ^{2}}

\frac{x + 1}{x ^{6} + 23 x ^{5} + 210 x ^{4} + 968 x ^{3} + 2368 x ^{2} + 2928 x + 1440}

求解步骤

\frac{x + 1}{( x + 2 ) ^{3} ( x + 5 ) ( x + 6 ) ^{2}}

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

= \frac{x + 1}{( x ^{3} + 6 x ^{2} + 12 x + 8 ) ( x + 5 ) ( x + 6 ) ^{2}}

(x + 6)^{2} = x^{2} + 12 x + 36

= \frac{x + 1}{( x ^{3} + 6 x ^{2} + 12 x + 8 ) ( x + 5 ) ( x ^{2} + 12 x + 36 )}

乘开

(x^{3} + 6 x^{2} + 12 x + 8) (x + 5) (x^{2} + 12 x + 36) : x^{6} + 23 x^{5} + 210 x^{4} + 968 x^{3} + 2368 x^{2} + 2928 x + 1440

= \frac{x + 1}{x ^{6} + 23 x ^{5} + 210 x ^{4} + 968 x ^{3} + 2368 x ^{2} + 2928 x + 1440}

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

e x p an d (\frac{( 4 x ^{4} - 1 ) ^{2}}{16 x ^{4}}) + 1

e x p an d \frac{3 a ^{3} t}{( 7 a ^{2} + t ^{2} )}

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

e x p an d \frac{7 x ( x ^{2} + 9 )}{( 1 + 4 x ^{2} ) ( 4 - 5 x ^{3} )}