展开 ((x^2+3x+5)^n+x^2(x+3)^2+3)/(x^2+3x+4)

解答

展开

\frac{( x ^{2} + 3 x + 5 ) ^{n} + x ^{2} ( x + 3 ) ^{2} + 3}{x ^{2} + 3 x + 4}

\frac{( x ^{2} + 3 x + 5 ) ^{n} + x ^{4} + 6 x ^{3} + 9 x ^{2} + 3}{x ^{2} + 3 x + 4}

求解步骤

\frac{( x ^{2} + 3 x + 5 ) ^{n} + x ^{2} ( x + 3 ) ^{2} + 3}{x ^{2} + 3 x + 4}

(x + 3)^{2} = x^{2} + 6 x + 9

= \frac{( x ^{2} + 3 x + 5 ) ^{n} + x ^{2} ( x ^{2} + 6 x + 9 ) + 3}{x ^{2} + 3 x + 4}

乘开

(x^{2} + 3 x + 5)^{n} + x^{2} (x^{2} + 6 x + 9) + 3 : (x^{2} + 3 x + 5)^{n} + x^{4} + 6 x^{3} + 9 x^{2} + 3

= \frac{( x ^{2} + 3 x + 5 ) ^{n} + x ^{4} + 6 x ^{3} + 9 x ^{2} + 3}{x ^{2} + 3 x + 4}

e x p an d (2 x e^{y} + e^{x}) d x + (x^{2} + 1) e^{y} d y

e x p an d (x^{2} y^{2} + 1) d x + 2 x^{2} d y

e x p an d (2, 5) y (0, - 3)

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

e x p an d \frac{3 t ^{2} - 8 t + 5}{( t + 1 ) ^{4}}