Fill in the blank to make equivalent rational expressions. \( \frac{8}{v+5}=\frac{1}{(v-8)(v+5)} \)

To make the expressions equivalent, we need to have the same denominator. The given expressions have the denominator of the left side as \( v + 5 \), and the denominator on the right side as \( (v - 8)(v + 5) \). To achieve this, we can multiply the numerator on the left side by \( (v - 8) \). This gives us: \[\frac{8(v - 8)}{(v + 5)(v - 8)} = \frac{8v - 64}{(v + 5)(v - 8)}\] Now, both sides have the denominator \( (v - 8)(v + 5) \), which makes the expressions equivalent when we write: \[\frac{8(v - 8)}{(v - 8)(v + 5)} = \frac{1}{(v - 8)(v + 5)}\] So, the filled-in blank for the right side to make it equivalent would be \( 8(v-8) \).