Question

(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a. find x..????

Answer 1

\[\frac{ (x-a) }{ (x-b) }+\frac{ (x-b) }{ (x-a) }=\frac{ a }{ b }+\frac{ b }{ a }\]

Answer 2

Were you given any values?

Answer 3

Let $x = a + b$ or let $x = 0$. Then see what you get.

Answer 4

Oops. I used dollar signs. My bad.

Answer 5

No worries, ML is here! haha! :)

Answer 6

how can we take a+b=x or x=0. at wat basis...???

Answer 7

By observation.

Answer 8

If you let:\[u=x-a\]\[v=x-b\]then you get:\[\frac{u}{v}+\frac{v}{u}=\frac{a}{b}+\frac{b}{a}\]Now, by observation we see that the only possible solutions to this are:\[u=a\text{ and }v=b\tag{1}\]\[u=-a\text{ and }v=-b\tag{2}\]\[u=b\text{ and }v=a\tag{3}\]\[u=-b\text{ and }v=-a\tag{4}\]For (1) we get:\[x=2a\text{ and }x=2b\]This is inconsistent and can therefore be rejected.
For (2) we get:\[x=0\text{ and }x=0\]which is a consistent solution and is therefore valid.

Use the same reasoning for (3) and (4) and you should get all the valid solutions.