What is ((x^3)/6+1/(2x))((x^2)/2+1/(2x^2)) ?

The solution to ((x^3)/6+1/(2x))((x^2)/2+1/(2x^2)) is ((x^4+3)(x^4+1))/(12x^3)

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simplify ((x^3)/6+1/(2x))((x^2)/2+1/(2x^2))

simplify

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

\frac{( x ^{4} + 3 ) ( x ^{4} + 1 )}{12 x ^{3}}

Solution steps

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

Join

\frac{x ^{3}}{6} + \frac{1}{2 x} : \frac{x ^{4} + 3}{6 x}

= \frac{x ^{4} + 3}{6 x} (\frac{x ^{2}}{2} + \frac{1}{2 x ^{2}})

Apply the fraction rule:

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

= \frac{( x ^{4} + 3 ) ( \frac{x ^{2}}{2} + \frac{1}{2 x ^{2}} )}{6 x}

Simplify

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

= \frac{\frac{( x ^{4} + 3 ) ( x ^{4} + 1 )}{2 x ^{2}}}{6 x}

Apply the fraction rule:

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

= \frac{( x ^{4} + 3 ) ( x ^{4} + 1 )}{2 x ^{2} \cdot 6 x}

Simplify

2 x^{2} \cdot 6 x : 12 x^{3}

= \frac{( x ^{4} + 3 ) ( x ^{4} + 1 )}{12 x ^{3}}

(2 cos (x) + 1) (cos (x) - 1)

A (1, 4) N (- 3, - 2)

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

t^{2} (2 t^{3} - 5)^{4} d x

(2 + t) (9 - t^{2})

What is ((x^3)/6+1/(2x))((x^2)/2+1/(2x^2)) ?
The solution to ((x^3)/6+1/(2x))((x^2)/2+1/(2x^2)) is ((x^4+3)(x^4+1))/(12x^3)