factorize
Asked by YogeshTekam | 6th Nov, 2012, 08:05: AM
Expert Answer:
(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
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
Answered by | 6th Nov, 2012, 09:22: PM
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