Solve for \( y \). \[ \frac{y+5}{10 y}+\frac{3}{4}=\frac{1}{y} \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( y=\square \)

To solve the equation \[ \frac{y+5}{10y} + \frac{3}{4} = \frac{1}{y}, \] we start by eliminating the fractions. To do this, we can multiply both sides by \( 40y \) (the least common multiple of the denominators): \[ 40y \left( \frac{y+5}{10y} \right) + 40y \left( \frac{3}{4} \right) = 40y \left( \frac{1}{y} \right). \] This simplifies to: \[ 4(y + 5) + 30y = 40. \] Expanding this gives: \[ 4y + 20 + 30y = 40. \] Combining like terms results in: \[ 34y + 20 = 40. \] Next, we isolate \( y \): \[ 34y = 40 - 20, \] \[ 34y = 20, \] \[ y = \frac{20}{34} = \frac{10}{17}. \] Thus, the solution is: \[ y = \frac{10}{17}. \]