Question

Solve for x (in terms of "a" and "b") :

$\frac{a}{x - b} - \frac{b}{x -a} = 2 \: \: where \: x \: is \: not \: equal \: to \: a \: and \: b$
If anyone knows it's answer

Then pls answer it....!!!!

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Answer 1

Answer:

Here is your answer

a/x-b + b/x-a = 2

a(x-a) + b(x-b) = 2

(x-a)(x-b)

ax - a^2 + bx - b^2 = 2x^2 - 2bx - 2ax + 2ab

2x^2 - 2bx - bx - 2ax -ax +a^2 + b^2 + 2ab =0

2 x^2 - 3bx - 3ax + (a+ b)^2 = 0

2x^2 - 3x(a+b) + (a+b)(a+b) = 0

2x^2 -2x(a+b) -x(a+b) +(a+b)(a+b) = 0

2x[ x - (a+b)] -(a+b)[ x - (a+b)] = 0

[2x -(a+b)] [ x - (a+b) ] = 0

Now,

[2x-(a+b)] = 0

2x = a+b

x= a+b/2✔️

and

[ x - (a+b)] = 0

x = a+b✔️