# How do you solve \frac { v + 1} { v } = \frac { 8} { 10}?

$v = - 5$
Cross-multiply to get $10 \left(v + 1\right) = 8 v$, or $10 v + 10 = 8 v$. Now subtract $8 v$ from both sides and subtract $10$ to get $2 v = - 10$. Diving both sides by $2$ leads to $v = - 5$.
$\frac{v + 1}{v} = \frac{- 5 + 1}{- 5} = \frac{- 4}{- 5} = \frac{\cancel{- 1} \cdot 4}{\cancel{- 1} \cdot 5} = \frac{4}{5} = \frac{2 \cdot 4}{2 \cdot 5} = \frac{8}{10}$.