展开 (3(x+3)(x+5))/(x^6)

解答

展开

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

\frac{3}{x ^{4}} + \frac{24}{x ^{5}} + \frac{45}{x ^{6}}

求解步骤

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

乘开

3 (x + 3) (x + 5) : 3 x^{2} + 24 x + 45

= \frac{3 x ^{2} + 24 x + 45}{x ^{6}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{3 x ^{2} + 24 x + 45}{x ^{6}} = \frac{3 x ^{2}}{x ^{6}} + \frac{24 x}{x ^{6}} + \frac{45}{x ^{6}}

= \frac{3 x ^{2}}{x ^{6}} + \frac{24 x}{x ^{6}} + \frac{45}{x ^{6}}

消掉

\frac{3 x ^{2}}{x ^{6}} : \frac{3}{x ^{4}}

= \frac{3}{x ^{4}} + \frac{24 x}{x ^{6}} + \frac{45}{x ^{6}}

消掉

\frac{24 x}{x ^{6}} : \frac{24}{x ^{5}}

= \frac{3}{x ^{4}} + \frac{24}{x ^{5}} + \frac{45}{x ^{6}}

e x p an d \frac{( 3 x + 2 y ) ^{3}}{x}

e x p an d \frac{( - 3 x - 8 ) ( x - 1 )}{9}

e x p an d \frac{( x ^{2} - 9 ) ( x - 2 )}{3 x + 6}

e x p an d \frac{2 A - 3}{2 ( A - 1 )}

e x p an d L im x \Rightarrow 3 (2 x - 3)