展开 ((a^2+4)^2)/(4a)

解答

展开

\frac{( a ^{2} + 4 ) ^{2}}{4 a}

\frac{a ^{3}}{4} + 2 a + \frac{4}{a}

求解步骤

\frac{( a ^{2} + 4 ) ^{2}}{4 a}

(a^{2} + 4)^{2} = a^{4} + 8 a^{2} + 16

= \frac{a ^{4} + 8 a ^{2} + 16}{4 a}

使用分式法则:

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

\frac{a ^{4} + 8 a ^{2} + 16}{4 a} = \frac{a ^{4}}{4 a} + \frac{8 a ^{2}}{4 a} + \frac{16}{4 a}

= \frac{a ^{4}}{4 a} + \frac{8 a ^{2}}{4 a} + \frac{16}{4 a}

消掉

\frac{a ^{4}}{4 a} : \frac{a ^{3}}{4}

= \frac{a ^{3}}{4} + \frac{8 a ^{2}}{4 a} + \frac{16}{4 a}

消掉

\frac{8 a ^{2}}{4 a} : 2 a

= \frac{a ^{3}}{4} + 2 a + \frac{16}{4 a}

数字相除:

\frac{16}{4} = 4

= \frac{a ^{3}}{4} + 2 a + \frac{4}{a}

e x p an d A (2, 4) B (- 8, - 12)

e x p an d \frac{- 2 e ^{- x^{2}} x ^{3} - 4 e ^{- x^{2}}}{( x ^{2} + 1 ) ^{e}}

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

\frac{d}{d t} ((A (t)) (12 - \frac{5 A ( t )}{500 - t}))

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