Find $x$ if $\displaystyle \frac{2}{x} - \frac{3}{5} + \frac{1}{x} = \frac{1}{5}$.
To solve for $x$, I need to clear the fractions by multiplying both sides of the equation by a common denominator. The lowest common denominator of all the fractions is $5x$, so I will multiply both sides by $5x$ and simplify. This gives me $10 - 3x + 5 = x$. Now I have a linear equation in $x$ that I can solve by combining like terms and isolating $x$. Combining like terms, I get $15 - 3x = x$. Adding $3x$ to both sides, I get $15 = 4x$. Dividing both sides by $4$, I get $x = \frac{15}{4}$. 