展开 (-2x^2+289)/((x^2+289)^{5/2)}

解答

展开

\frac{- 2 x ^{2} + 289}{( x ^{2} + 289 ) ^{\frac{5}{2}}}

- \frac{2 x ^{2}}{( x ^{2} + 289 ) ^{\frac{5}{2}}} + \frac{289}{( x ^{2} + 289 ) ^{\frac{5}{2}}}

求解步骤

\frac{- 2 x ^{2} + 289}{( x ^{2} + 289 ) ^{\frac{5}{2}}}

使用分式法则:

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

\frac{- 2 x ^{2} + 289}{( x ^{2} + 289 ) ^{\frac{5}{2}}} = - \frac{2 x ^{2}}{( x ^{2} + 289 ) ^{\frac{5}{2}}} + \frac{289}{( x ^{2} + 289 ) ^{\frac{5}{2}}}

= - \frac{2 x ^{2}}{( x ^{2} + 289 ) ^{\frac{5}{2}}} + \frac{289}{( x ^{2} + 289 ) ^{\frac{5}{2}}}

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

s im pl i f y 5 (\frac{x ^{2}}{2} - \frac{2 x ^{3}}{3}) + 3000

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

e x p an d (2 - 2 π x)^{2}

e x p an d - \frac{5}{12 ( x + 2 )} + \frac{5 x - 8}{12 ( x ^{2} - 2 x + 4 )}