Algebra Examples

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

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

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

Step 1.2

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

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

Step 1.3

Rewrite the polynomial.

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

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

Step 1.4

Factor using the perfect square trinomial rule

a^{2} - 2 a b + b^{2} = {(a - b)}^{2}

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where

a = m

$a = m$ and

b = 1

$b = 1$ .

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

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

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

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

Step 2

Cancel the common factor of

${(m - 1)}^{2}$ and

$m - 1$ .

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Step 2.1

Factor

$m - 1$ out of

${(m - 1)}^{2}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by

$1$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.2.4

Divide

$m - 1$ by

$1$ .

$m - 1$