What is expand 1/(2u^3)(u*1/2 x-v+u^3=0) ?

The solution to expand 1/(2u^3)(u*1/2 x-v+u^3=0) is x/(4u^2)-v/(2u^3)+1/2 =0

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expand 1/(2u^3)(u*1/2 x-v+u^3=0)

expand

\frac{1}{2 u ^{3}} (u \cdot \frac{1}{2} x - v + u^{3} = 0)

\frac{x}{4 u ^{2}} - \frac{v}{2 u ^{3}} + \frac{1}{2} = 0

Solution steps

\frac{1}{2 u ^{3}} (u \frac{1}{2} x - v + u^{3} = 0)

= \frac{1}{2 u ^{3}} (\frac{1}{2} ux - v + 0 = u^{3})

Distribute parentheses

\frac{1}{2 u ^{3}} u \frac{1}{2} x + \frac{1}{2 u ^{3}} (- v) + \frac{1}{2 u ^{3}} u^{3} = 0

Apply minus-plus rules

+ (- a) = - a

\frac{1}{2} \cdot \frac{1}{2 u ^{3}} ux - \frac{1}{2 u ^{3}} v + \frac{1}{2 u ^{3}} u^{3} = 0

Expand

\frac{1}{2} \cdot \frac{1}{2 u ^{3}} ux - \frac{1}{2 u ^{3}} v + \frac{1}{2 u ^{3}} u^{3} : \frac{x}{4 u ^{2}} - \frac{v}{2 u ^{3}} + \frac{1}{2}

\frac{x}{4 u ^{2}} - \frac{v}{2 u ^{3}} + \frac{1}{2} = 0

(sinh (x)) (coth^{2} (x) + csch^{3} (x)) d x

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

t^{2} (a t + b) e^{t}

\frac{2 ( 3Δ x - 2 x - 1 )}{Δ x ( 1 - 2 x - 2Δ x ) ( 1 - 2 x )}

\frac{6 x ^{2} + 7 x - 3}{x ^{2} ( x + 5 )}

What is expand 1/(2u^3)(u*1/2 x-v+u^3=0) ?
The solution to expand 1/(2u^3)(u*1/2 x-v+u^3=0) is x/(4u^2)-v/(2u^3)+1/2 =0