What is (3x^{-3}+4x)/(2x-x^{-2)} ?

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

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simplify (3x^{-3}+4x)/(2x-x^{-2)}

simplify

\frac{3 x ^{- 3} + 4 x}{2 x - x ^{- 2}}

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

Solution steps

\frac{3 x ^{- 3} + 4 x}{2 x - x ^{- 2}}

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

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

Join

\frac{3}{x ^{3}} + 4 x : \frac{3 + 4 x ^{4}}{x ^{3}}

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

Apply the fraction rule:

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

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

Apply exponent rule:

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

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

Join

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

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

Multiply

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

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

9 m^{2}

4 \frac{5}{6}

4 \times (- 8)

- 100 + - 9 + 9 - - 16

- \frac{1}{2} \div \frac{3}{2}

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