Solve the following equations. 5. \( \frac{1}{5 x}=\frac{3}{x}+\frac{1}{5} \)

To solve the equation \( \frac{1}{5 x} = \frac{3}{x} + \frac{1}{5} \), we first find a common denominator, which is \( 5x \). This allows us to rewrite the equation as: \[ \frac{1}{5x} = \frac{15}{5x} + \frac{x}{5x} \] Now, we combine the terms on the right side: \[ \frac{1}{5x} = \frac{15 + x}{5x} \] Since the denominators are the same, we can equate the numerators: \[ 1 = 15 + x \] To isolate \( x \), subtract 15 from both sides: \[ x = 1 - 15 \] Thus, \[ x = -14 \] The solution to the equation is \( x = -14 \).