展开 (3(x^2+2)^{4/3}+3)/(2(x^2+2)^{1/3)}

解答

展开

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

\frac{3 x ^{2} + 6}{2} + \frac{3}{2 ( x ^{2} + 2 ) ^{\frac{1}{3}}}

求解步骤

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

使用分式法则:

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

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

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

消掉

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

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

乘开

3 (x^{2} + 2) : 3 x^{2} + 6

= \frac{3 x ^{2} + 6}{2} + \frac{3}{2 ( x ^{2} + 2 ) ^{\frac{1}{3}}}

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

e x p an d (b^{2} + c^{2})^{2} + a^{2}

\frac{d ^{2}}{d x ^{2}} ((u (x)) (5.38 + 1.25 \cdot ln (x) - 250 x))

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

e x p an d 2 π (64 - 322)