展开 (4x(x^3+2)+3x^2)/(2(x^3+2)^{1/2)}

解答

展开

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

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

求解步骤

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

乘开

4 x (x^{3} + 2) + 3 x^{2} : 4 x^{4} + 8 x + 3 x^{2}

= \frac{4 x ^{4} + 8 x + 3 x ^{2}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}}

使用分式法则:

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

\frac{4 x ^{4} + 8 x + 3 x ^{2}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}} = \frac{4 x ^{4}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}} + \frac{8 x}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}} + \frac{3 x ^{2}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}}

= \frac{4 x ^{4}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}} + \frac{8 x}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}} + \frac{3 x ^{2}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}}

数字相除:

\frac{4}{2} = 2

= \frac{2 x ^{4}}{( x ^{3} + 2 ) ^{\frac{1}{2}}} + \frac{8 x}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}} + \frac{3 x ^{2}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}}

数字相除:

\frac{8}{2} = 4

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

e x p an d (17 - 3) (6 + 2)

e x p an d \frac{s ^{2} + 12}{( s ^{2} + 9 ) ( x + 2 ) ( x + 1 ) ( x - 1 )}

e x p an d 6 (4 a)

e x p an d \frac{12 x - 4 x ^{2}}{( x + 3 ) ^{2}}

e x p an d n o t ab l e (a - ab)^{2}