Question

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

Answer 1

$\frac{2x+4}{2x+1}=\frac{2x+1}{2x+4}$
Sum of numerators of both sides $=2x+4+2x+1=4x+5$
Sum of denominators in both sides $=2x+1+2x+4=4x+5$
Two sums are equal , so by the formula
$4x+5=0$
$\Rightarrow 4x=-5$
$\Rightarrow x=\frac{-5}{4}$