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

The solution to (x^2+1/(x^2))(x^3+1/(x^3)) is ((x^4+1)(x^6+1))/(x^5)

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

simplify

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

\frac{( x ^{4} + 1 ) ( x ^{6} + 1 )}{x ^{5}}

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

x^{3} x^{2} : x^{5}

= \frac{( x ^{4} + 1 ) ( x ^{6} + 1 )}{x ^{5}}

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

5 + 6

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

\frac{2 ( x + 9 ) ( x + 1 )}{( x + 4 ) ( x - 2 )}

x (x - 2 y)

What is (x^2+1/(x^2))(x^3+1/(x^3)) ?
The solution to (x^2+1/(x^2))(x^3+1/(x^3)) is ((x^4+1)(x^6+1))/(x^5)