Answer
$\frac{v + 7}{v - 8}$
Work Step by Step
Let's factor the denominators first:
$\frac{v + 5}{(v - 11)(v + 5)} \div \frac{v - 8}{(v - 11)(v + 7)}$
To divide two expressions, we multiply the first one with the reciprocal of the second one:
$\frac{v + 5}{(v - 11)(v + 5)} • \frac{(v - 11)(v + 7)}{v - 8}$
Combine the two rational expressions into one:
$\frac{(v + 5)(v - 11)(v + 7)}{(v - 11)(v + 5)(v - 8)}$
Now, we want to cancel out the factors that are common in the numerators and denominators of each rational expression:
$\frac{v + 7}{v - 8}$
