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

Question

9071 views around the world

You can reuse this answer
Creative Commons License

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)#