What is expand ((y^2+1)(y^4-y^2+1))/(2y^3) ?

The solution to expand ((y^2+1)(y^4-y^2+1))/(2y^3) is (y^3)/2+1/(2y^3)

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expand ((y^2+1)(y^4-y^2+1))/(2y^3)

expand

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

\frac{y ^{3}}{2} + \frac{1}{2 y ^{3}}

Solution steps

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

Expand

(y^{2} + 1) (y^{4} - y^{2} + 1) : y^{6} + 1

= \frac{y ^{6} + 1}{2 y ^{3}}

Apply the fraction rule:

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

\frac{y ^{6} + 1}{2 y ^{3}} = \frac{y ^{6}}{2 y ^{3}} + \frac{1}{2 y ^{3}}

= \frac{y ^{6}}{2 y ^{3}} + \frac{1}{2 y ^{3}}

Cancel

\frac{y ^{6}}{2 y ^{3}} : \frac{y ^{3}}{2}

= \frac{y ^{3}}{2} + \frac{1}{2 y ^{3}}

- \frac{120}{( 3 - 1 ) ^{6}} - cos (3 - 1)

(3 tan^{2} (x) - 1) (tan^{2} (x) - 3)

(x - 2 i) (x + 2 i)

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

cot (x) + cos (x) (tan (x) - tan (\frac{x}{2}))

What is expand ((y^2+1)(y^4-y^2+1))/(2y^3) ?
The solution to expand ((y^2+1)(y^4-y^2+1))/(2y^3) is (y^3)/2+1/(2y^3)