Let ‘x’ be the base or radix of the number system .
The equation is : $\dfrac{3.x^{2}+1.x^{1} +2.x^{0} }{2.x^{1}+0.x^0} =1.x^{1} +3.x^{0}+1.x^{-1}$
$\qquad \implies \dfrac{3.x^{2}+x +2}{2.x}=x+3 +1/x$
$\qquad \implies \dfrac{3.x^{2}+x +2}{2.x}=\dfrac{x^{2}+3x +1}{x}$
$\qquad \implies 3.x^{2}+x +2=2.x^{2}+6x +2$
$\qquad \implies x^{2}+-5x = 0$
$\qquad \implies x(x-5) = 0$
$\qquad \implies x = 0 \text{ or } x = 5$
As base or radix of a number system cannot be zero, here x = 5.