Question

Using the sutra shunyam samyasachchaye, solve the equations.
$\frac{1}{x+2}+\frac{1}{x+6}=\frac{1}{x+1}+\frac{1}{x+7}$

Answer 1

Sum of denominators of L.H.S $=x+2+x+6=2x+8$ ........(i)
Sum of denominators of R.H.S $=x+1+x+7=2x+8$ ............(ii)
(i) and (ii) are equal so by formula
$2x+8=0$
$\Rightarrow 2x=-8$
$\Rightarrow x=-4$