problem: Find $x$ if $\displaystyle \frac{2}{x} - \frac{3}{5} + \frac{1}{x} = \frac{1}{5}$.
solution: We first combine the two fractions with $x$ in the denominator to give $\frac{3}{x} - \frac{3}{5} = \frac{1}{5}$.  Adding $\frac{3}{5}$ to both sides gives us $\frac{3}{x} = \frac{4}{5}$.  Cross-multiplying this equation (or multiplying both sides by $5x$) gives $4x = 15$.  Dividing both sides of this equation by $4$ gives us $x =\boxed{\frac{15}{4}}$.