An algebra problem by Aakhyat Singh

$3f(x)+5f\left(\dfrac{1}{x}\right)=-3+\dfrac{1}{x} \phantom{cccccccc} (1)$

If we set $x\mapsto \dfrac{1}{x}$ in $(1)$ we get

$3f\left(\dfrac{1}{x}\right)+5f(x)=-3+x\phantom{cccccicccc} (2)$

From $5(2)-3(1)$

$15f\left(\dfrac{1}{x}\right)+25f(x)-9f(x)-15f\left(\dfrac{1}{x}\right)=-15+5x+9-\dfrac{3}{x}$

Simplifying like terms and solving for $f(x)$

$f(x)=\boxed{\dfrac{5x-6-\dfrac{3}{x}}{16}}$