Simplify the rational expression (u+5v)÷(8v²u²-6v)÷(8v²u²)

First, note that since the denominators are the same for both factors, we can simply subtract the numerators.

Numerator :

(u + 5v) - (u - 6v) = u + 5v - u + 6v = 11v

Here, be sure to distribute the subtraction sign to both parts of the second factor!

Denominator :

8v^2u^2

Now, combine to get :

11v / 8v^2u^2

Both the numerator and denominator have a factor of v that can be cancelled out. Simplify as follows

11v / 8v^2u^2 = 11 * v / 8vu^2 * v = 11 / 8vu^2 * v/v = 11 / 8vu^2 * 1 = 11 / 8vu^2