展开 ((a^2-2x^2))/((x^2+a^2)^{5/2)}

解答

展开

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

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

求解步骤

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

使用分式法则:

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

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

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

e x p an d \frac{2 sec ^{2} ( x )}{( tan ( x ) - 1 ) ^{2}}

e x p an d \frac{- x ^{2} + 2 x - 5}{( x + 1 ) ( x ^{2} + 6 x + 9 )}

e x p an d \frac{10 s - 15}{( 1 + s ) ( 2 s + 1 )}

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

e x p an d \frac{x - 6}{x ( x + 6 )}