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

The solution to expand ((1-1/(x^3+2)))/((x+1/(x-1))) is (x^2-1)/(x^3+\sqrt[3]{2)*2^{2/3}}

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expand ((1-1/(x^3+2)))/((x+1/(x-1)))

expand

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

Solution steps

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

Join

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

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

Join

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

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

Divide fractions:

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

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

Factor

(x - 1) (x^{3} + 1) : (x + 1) (x - 1) (x^{2} - x + 1)

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

Factor

Cancel the common factor:

x^{2} - x + 1

Expand

(x + 1) (x - 1) : x^{2} - 1

(x - 1 + i 2)^{2} \cdot (x + 1 + i 2)^{2}

lo g_{x} (\frac{y}{3 z})

(x - 5) (x + 5)

x^{2} (1 + 1 - x^{2})

\frac{( 3 x ^{4} )}{( 8 x ^{5} - 3 ) ^{4}}

What is expand ((1-1/(x^3+2)))/((x+1/(x-1))) ?
The solution to expand ((1-1/(x^3+2)))/((x+1/(x-1))) is (x^2-1)/(x^3+\sqrt[3]{2)*2^{2/3}}