展开 (4x+1)/((x+1)^3(x^2+6)^2)

解答

展开

\frac{4 x + 1}{( x + 1 ) ^{3} ( x ^{2} + 6 ) ^{2}}

\frac{4 x + 1}{x ^{7} + 3 x ^{6} + 15 x ^{5} + 37 x ^{4} + 72 x ^{3} + 120 x ^{2} + 108 x + 36}

求解步骤

\frac{4 x + 1}{( x + 1 ) ^{3} ( x ^{2} + 6 ) ^{2}}

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

= \frac{4 x + 1}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x ^{2} + 6 ) ^{2}}

(x^{2} + 6)^{2} = x^{4} + 12 x^{2} + 36

= \frac{4 x + 1}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x ^{4} + 12 x ^{2} + 36 )}

乘开

(x^{3} + 3 x^{2} + 3 x + 1) (x^{4} + 12 x^{2} + 36) : x^{7} + 3 x^{6} + 15 x^{5} + 37 x^{4} + 72 x^{3} + 120 x^{2} + 108 x + 36

= \frac{4 x + 1}{x ^{7} + 3 x ^{6} + 15 x ^{5} + 37 x ^{4} + 72 x ^{3} + 120 x ^{2} + 108 x + 36}

e x p an d - \frac{2 x ^{4} + 36 x ^{3} + 243 x ^{2} + 732 x + 838}{( x + 4 ) ^{4}}

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

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

e x p an d - 2 (100)^{2} + 400 (100) - 2000

e x p an d 2 (3 x + 2) (2 x + 3) - (3 x +, 1) (4 x + 3)