What is expand ((1-v^2)dv)/(v(1+v^2)) ?

The solution to expand ((1-v^2)dv)/(v(1+v^2)) is (dv-v^2dv)/(v+v^3)

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expand ((1-v^2)dv)/(v(1+v^2))

expand

\frac{( 1 - v ^{2} ) d v}{v ( 1 + v ^{2} )}

\frac{d v - v ^{2} d v}{v + v ^{3}}

Solution steps

\frac{( 1 - v ^{2} ) d v}{v ( 1 + v ^{2} )}

Expand

v (1 + v^{2}) : v + v^{3}

= \frac{( - v ^{2} + 1 ) d v}{v + v ^{3}}

Expand

(1 - v^{2}) d v : d v - v^{2} d v

= \frac{d v - v ^{2} d v}{v + v ^{3}}

\frac{( n ! + 1 ) ^{3}}{( 8 n + 1 ) !}

\frac{( 5 x + 2 ) ( 2 x + 1 )}{( x - 3 ) ( x + 3 )}

\frac{1}{2} sin (2 (x + t)) + \frac{1}{2} sin (2 (x - t))

(19417600 = 6000000 \cdot t + 46000000) \cdot 0.0269

- 5 (x + 3 y = 13)

What is expand ((1-v^2)dv)/(v(1+v^2)) ?
The solution to expand ((1-v^2)dv)/(v(1+v^2)) is (dv-v^2dv)/(v+v^3)