smc

Both terms have a $-\frac{7}{x-3}$ term, so add $\frac{7}{x-3}$ to both sides. This results in $x=3$. However, note that if $3$ is plugged back into the original equation, it results in $$3-\frac{7}{0}=3-\frac{7}{0}$$ Since dividing by zero is undefined, $3$ is an extraneous solution. That means there are no solutions, so the answer is $\boxed{\text{no root}}$.