Simplify (m^2-2m+1)/(m-1)

$\frac{m^{2} - 2 m + 1}{m - 1}$

Step 1

Factor using the perfect square rule.

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

$\frac{m^{2} - 2 m + 1^{2}}{m - 1}$

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

$2 m = 2 \cdot m \cdot 1$

Rewrite the polynomial.

$\frac{m^{2} - 2 \cdot m \cdot 1 + 1^{2}}{m - 1}$

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

$\frac{{(m - 1)}^{2}}{m - 1}$

Step 2

Cancel the common factor of ${(m - 1)}^{2}$ and $m - 1$ .

Factor $m - 1$ out of ${(m - 1)}^{2}$ .

$\frac{(m - 1) (m - 1)}{m - 1}$

Cancel the common factors.

Multiply by $1$ .

$\frac{(m - 1) (m - 1)}{(m - 1) \cdot 1}$

Cancel the common factor.

$\frac{(m - 1) (m - 1)}{(m - 1) \cdot 1}$

Rewrite the expression.

$\frac{m - 1}{1}$

Divide $m - 1$ by $1$ .

$m - 1$