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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 1

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

\frac{6}{5} + \frac{7}{8}

5 p^{3} - 10 p^{2} + 3 p - 6

y^{5} \cdot y^{2}

\frac{5}{1 - 2 i}

\frac{5 x - 5}{x - 5}