# How do you simplify (x^2-2x+1)/(x^2-1)?

Sep 20, 2015

I found $\frac{x - 1}{x + 1}$

#### Explanation:

When we look at ${x}^{2} - 2 x + 1$ it resembles square of something which is

${\left(x - 1\right)}^{2}$ = ${x}^{2} - 2 x + 1$

According to this rule: ${a}^{2} - {b}^{2} = \left(a - b\right) . \left(a + b\right)$

${x}^{2} - 1 = \left(x - 1\right) . \left(x + 1\right)$

$\frac{{x}^{2} - 2 x + 1}{{x}^{2} - 1} = {\left(x - 1\right)}^{2} / \left(\left(x - 1\right) \left(x + 1\right)\right)$

So ${\left(x - 1\right)}^{2} \mathmr{and} \left(x - 1\right)$ simplify each other. Then we find:

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