What is (3x^3-3x)/(x^5-x) ?

The solution to (3x^3-3x)/(x^5-x) is 3/(x^2+1)

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simplify (3x^3-3x)/(x^5-x)

simplify

\frac{3 x ^{3} - 3 x}{x ^{5} - x}

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

Solution steps

\frac{3 x ^{3} - 3 x}{x ^{5} - x}

Factor

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

= \frac{3 x ( x + 1 ) ( x - 1 )}{x ^{5} - x}

Factor

x^{5} - x : x (x^{2} + 1) (x + 1) (x - 1)

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

Cancel the common factor:

x

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

Cancel the common factor:

x + 1

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

Cancel the common factor:

x - 1

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

2 i \cdot (- i)

(3 + 2 i) - (4 + 2 i)

\frac{1}{9} - \frac{1}{27}

2 \cdot 33

(- \frac{3}{7})^{2}