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