Question

some intelligent person tells the answer pls. - q. a/(x-b)+b/(x-a)=2​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO SOLVE

$\displaystyle \: \frac{a}{x - b} + \frac{b}{x - a} = 2$

EVALUATION

$\displaystyle \: \frac{a}{x - b} + \frac{b}{x - a} = 2$

$\implies \: \displaystyle \: \frac{a}{x - b} - 1 + \frac{b}{x - a} - 1 = 0$

$\implies \: \displaystyle \: \frac{a - x + b}{x - b} + \frac{b - x + a}{x - a} = 0$

$\implies \: \displaystyle \: (a + b - x) \bigg [\frac{1}{x - b} + \frac{1}{x - a} \bigg] \: = 0$

So

$\displaystyle \:Either \: (a + b - x) = 0 \: \: or \: \bigg [\frac{1}{x - b} + \frac{1}{x - a} \bigg] \: = 0$

Now

$\displaystyle \: \: (a + b - x) = 0 \: \: gives \: \: x = a + b$

Again

$\displaystyle \bigg [\frac{1}{x - b} + \frac{1}{x - a} \bigg] \: = 0 \: gives \:$

$\displaystyle \frac{1}{x - b} = - \frac{1}{x - a}$

$\implies \: x - a = - x + b$

$\implies \: 2x = a + b$

$\displaystyle \: x = \frac{a + b}{2}$

RESULT

SO the required solution is

$\displaystyle \: \sf{\boxed { \:x = (a + b) \: , \: \frac{ a + b}{2} \: }}$