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{1}{2} + \frac{3}{32} (4 (0.5) - \frac{0. 5 ^{3}}{3})

\frac{1}{2} (1 + cos (4 x))

(1 - t)^{3}

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

\frac{2 ( 3 + 3 )}{3}

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)