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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Cancel the common factor:

x - 1

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

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

\frac{12 x - 3 y}{15 a + 10 b} \cdot \frac{21 a + 14 b}{20 x - 5 y}

1 \frac{1}{2} \cdot 3

- 1 + 6 x - 8 x + 4 - 2 x

\frac{y + 2}{( y + 2 ) ^{2}} \cdot \frac{y ^{2} - 4}{y}

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