Elementary Technical Mathematics

$$x= 2.$$
We have: $\frac{7}{x}-3=\frac{1}{x}$ By multiplying both sides by $x$ and grouping the like terms, we get $$\frac{7}{x}x-3x=\frac{1} {x}x\Longrightarrow 7-3x=1 \Longrightarrow 3x=6.$$ By dividing both sides by $3$, we have $$x= \frac{6}{3}=2.$$