Solve for \( v \) \[ \frac{7}{5 v}+\frac{2}{3 v}=1 \]

To solve for \( v \) in the equation \[ \frac{7}{5v} + \frac{2}{3v} = 1, \] we first find a common denominator for the fractions on the left side. The common denominator for \( 5v \) and \( 3v \) is \( 15v \). We can rewrite each term: \[ \frac{7}{5v} = \frac{7 \times 3}{5v \times 3} = \frac{21}{15v}, \] \[ \frac{2}{3v} = \frac{2 \times 5}{3v \times 5} = \frac{10}{15v}. \] Now substituting these back into the equation gives: \[ \frac{21}{15v} + \frac{10}{15v} = 1. \] Combine the fractions: \[ \frac{21 + 10}{15v} = \frac{31}{15v} = 1. \] Next, we can cross-multiply to solve for \( v \): \[ 31 = 15v. \] Now, divide both sides by 15: \[ v = \frac{31}{15}. \] Thus, the solution for \( v \) is \[ \boxed{\frac{31}{15}}. \]