Finite Math Examples

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

Step 1

Factor using the perfect square rule.

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Step 1.1

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

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

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.

$2 x = 2 \cdot x \cdot 1$

Step 1.3

Rewrite the polynomial.

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

Step 1.4

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

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{{(x - 1)}^{2}}{x - 1}$ by cancelling the common factors.

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Step 2.1.1

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

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

Step 2.1.2

Multiply by $1$ .

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

$\frac{x - 1}{1}$

Step 2.2

Divide $x - 1$ by $1$ .

$x - 1$