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

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Answer 1 · 2015-09-20T15:41:03

I found $(x-1)/(x+1)$

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

$(x - 1)^2$ = $x^2 - 2x + 1$

According to this rule: $a^2 - b^2 = (a - b).(a + b)$

$x^2 - 1 =(x - 1).(x + 1)$

$(x^2 - 2x + 1)/(x^2 - 1) = (x - 1)^2/((x - 1)(x + 1))$

So $(x - 1)^2 and (x - 1)$ simplify each other. Then we find:

$(x-1)/(x+1)$

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