展开 (x(3x+4))/(2(x+1)^{3/2)}

解答

展开

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

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

求解步骤

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

乘开

x (3 x + 4) : 3 x^{2} + 4 x

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

使用分式法则:

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

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

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

数字相除:

\frac{4}{2} = 2

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

e x p an d (f (x) = 2, x^{4} - 3 x^{2} + 5 x - 6) - (g (x) = 2 x^{2} - 7 x + 10)

s im pl i f y (m E + m (E - U))^{2}

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

e x p an d sin (2 x) (cos (5 x) cos (3 x) - sin (3 x) sin (x))

e x p an d x (1 + 3 x^{3})