What is (3-x^{-2})/(x^{-3)-x} ?

The solution to (3-x^{-2})/(x^{-3)-x} is (x(3x^2-1))/(1-x^4)

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simplify (3-x^{-2})/(x^{-3)-x}

simplify

\frac{3 - x ^{- 2}}{x ^{- 3} - x}

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

Solution steps

\frac{3 - x ^{- 2}}{x ^{- 3} - x}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- 3} = \frac{1}{x ^{3}}

= \frac{3 - x ^{- 2}}{\frac{1}{x ^{3}} - x}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- 2} = \frac{1}{x ^{2}}

= \frac{3 - \frac{1}{x ^{2}}}{\frac{1}{x ^{3}} - x}

Join

\frac{1}{x ^{3}} - x : \frac{1 - x ^{4}}{x ^{3}}

= \frac{3 - \frac{1}{x ^{2}}}{\frac{1 - x ^{4}}{x ^{3}}}

Join

3 - \frac{1}{x ^{2}} : \frac{3 x ^{2} - 1}{x ^{2}}

= \frac{\frac{3 x ^{2} - 1}{x ^{2}}}{\frac{1 - x ^{4}}{x ^{3}}}

Divide fractions:

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

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{x ^{3}}{x ^{2}} = x^{3 - 2}

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

Subtract the numbers:

3 - 2 = 1

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

9 x^{2} + 6 + 2 x^{2} - x - 10

\frac{1 + sin ( x )}{cos ^{2} ( x )}

(y^{2} - 4 y + 9) - (3 y^{2} - 6 y - 9)

6175 + 728

4 t^{2} + 4 t + 1

What is (3-x^{-2})/(x^{-3)-x} ?
The solution to (3-x^{-2})/(x^{-3)-x} is (x(3x^2-1))/(1-x^4)