Question

Using the sutra shunyam samyasachchaye, solve the equations.
$\frac{3x+2}{5x+7}+\frac{x+1}{3x-1}$

Answer 1

Sum of numerators of two sides $=3x+2+x+1=4x+3$ ..............(i)
Sum of denominators of two sides $=5x+7+3x-1=8x+6$ .............(ii)
Ratio of (i) and (ii) is $1:2$
$4x+3=0$
$\Rightarrow 4x=-3$
$\Rightarrow x=\frac{-3}{4}$