Question

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

Answer 1

Difference between numerator and denominator $=5x+7-2x-1=3x+6=3(x+2)$ .....(i)
Difference between numerator and denominator is R.H.S $=3x+5-x-1=2x+4=2(x+2)$ .......(ii)
Ratio of (i) and (ii) is $3:2$.
Thus, by formula
$3(x+2)=0$
$\Rightarrow x+2=0$
$\Rightarrow x=-2$