展开 (-2*x^2+1)/((x^2+1)^{5/2)}

解答

展开

\frac{- 2 \cdot x ^{2} + 1}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

- \frac{2 x ^{2}}{( x ^{2} + 1 ) ^{\frac{5}{2}}} + \frac{1}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

求解步骤

\frac{- 2 x ^{2} + 1}{( x ^{2} + 1 ) ^{\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} + 1}{( x ^{2} + 1 ) ^{\frac{5}{2}}} = - \frac{2 x ^{2}}{( x ^{2} + 1 ) ^{\frac{5}{2}}} + \frac{1}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

= - \frac{2 x ^{2}}{( x ^{2} + 1 ) ^{\frac{5}{2}}} + \frac{1}{( x ^{2} + 1 ) ^{\frac{5}{2}}}

e x p an d (10 x - 3 y = 3, 6) - (2 x + 5 y = - 4)

e x p an d \frac{6 e ^{- 5 π s} s + 1 - e ^{- 14 s} + 48 s}{s ( s ^{2} + 64 )}

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

e x p an d 5 (3 + 9)

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