展开 (-x+4)/(8x^{3/2)(x-2)^{3/4}}

解答

展开

\frac{- x + 4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

- \frac{1}{8 x ^{\frac{1}{2}} ( x - 2 ) ^{\frac{3}{4}}} + \frac{1}{2 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

求解步骤

\frac{- x + 4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

使用分式法则:

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

\frac{- x + 4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}} = - \frac{x}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}} + \frac{4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

= - \frac{x}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}} + \frac{4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

消掉

\frac{x}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}} : \frac{1}{8 x ^{\frac{1}{2}} ( x - 2 ) ^{\frac{3}{4}}}

= - \frac{1}{8 x ^{\frac{1}{2}} ( x - 2 ) ^{\frac{3}{4}}} + \frac{4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

消掉

\frac{4}{8 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}} : \frac{1}{2 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

= - \frac{1}{8 x ^{\frac{1}{2}} ( x - 2 ) ^{\frac{3}{4}}} + \frac{1}{2 x ^{\frac{3}{2}} ( x - 2 ) ^{\frac{3}{4}}}

s im pl i f y (x^{2} - x^{4} - 3 x^{2} + 1) (x^{2} + x^{4} - 3 x^{2} + 1)

s im pl i f y e^{(- 1 - i) t}

s im pl i f y (3 + x 3)^{2}

e x p an d \frac{1}{3} (1 = 3 A + B + (- 9) C + D) \frac{1}{3}

s im pl i f y (3 + 2 z i)^{2}