展开 (3x^2+4x)/(2(x+1)^{3/2)}

解答

展开

\frac{3 x ^{2} + 4 x}{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{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 s t e p (t - 2)

e x p an d (1 - 2 \cdot π \cdot i \cdot n)^{2}

e x p an d (4 + 9 x^{2}) d y - 9 - 4 y^{2}

s im pl i f y (x + 1 - \frac{9}{x - 1}) \cdot 2

s im pl i f y (x + 1) (x - \frac{1}{3})