Simplify (x^3-2x^2+x)/(x^3-x)

Factor ${\displaystyle x}$ out of ${\displaystyle x^3}$.

Factor ${\displaystyle x}$ out of ${\displaystyle -2x^2}$.

Raise ${\displaystyle x}$ to the power of ${\displaystyle 1}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x^1}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x\cdot x^2+x(-2x)}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x(x^2-2x)+x\cdot 1}$.

Rewrite ${\displaystyle 1}$ as ${\displaystyle 1^2}$.

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

Rewrite the polynomial.

Factor using the perfect square trinomial rule ${\displaystyle a^2-2ab+b^2={(a-b)}^2}$, where ${\displaystyle a=x}$ and ${\displaystyle b=1}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x^3}$.

Factor ${\displaystyle x}$ out of ${\displaystyle -x}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x\cdot x^2+x\cdot -1}$.

Cancel the common factor.

Rewrite the expression.

Factor ${\displaystyle x-1}$ out of ${\displaystyle {(x-1)}^2}$.

Cancel the common factors.