Question
Tue November 06, 2012 By: Yogeshtekam

factorize

Expert Reply
Tue November 06, 2012
(x-a)/(x-b) + (x-b)/(x-a) = a/b +b/a
multiply x-a
(x-a)^2/(x-b) + (x-b) = (a/b +b/a)(x-a)
multiply x-b
(x-a)^2 + (x-b)^2 =(a/b +b/a)(x-a)(x-b)
(x-a)^2 - (a/b +b/a)(x-a)(x-b) + (x-b)^2 = 0

[(x-a)-(a/b)(x-b)] [(x-a)-(b/a)(x-b)] = 0

So, (x-a)-(a/b)(x-b)=0
b(x-a)-a(x-b)=0
(b-a)x=0
x=0 

Also, (x-a)-(b/a)(x-b)=0
a(x-a)-b(x-b)=0
(a-b)x=a^2-b^2
(a-b)x=(a+b)(a-b)
x = a+b
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