Question

Using the sutra shunyam samyasachchaye, solve the equations.
$\frac{1}{x-4}+\frac{1}{x-6}=\frac{1}{x-2}+\frac{1}{x-8}$

Answer 1

Sum of denominators of L.H.S $=x-4+x-6=2x-10$ .......(i)
Sum of denominators of R.H.S $=x-2+x-8=2x-10$ .........(ii)
(i) and (ii) are same so by formula
$2x-10=0$
$\Rightarrow 2x=10$
$\Rightarrow x=5$