What is (\frac{x^3-x)/(x+1)}{(x-1)/(x+1)} ?

The solution to (\frac{x^3-x)/(x+1)}{(x-1)/(x+1)} is x(x+1)

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

simplify

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

x (x + 1)

Solution steps

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

Apply the fraction rule:

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

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

Cancel the common factor:

x + 1

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 1

= x (x + 1)

\frac{cos ( θ )}{cot ( θ )}

2 sin (t) cos (t)

\frac{\frac{9 - x ^{2}}{3 x}}{\frac{x ^{2} + 6 x + 9}{3 x}}

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

5 x 1 0^{- 3}

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