First, simplify the square roots:
√135 = √(9 x 15) = 3√15
√180 = √(36 x 5) = 6√5
√300 = √(100 x 3) = 10√3

Now, substitute these values into the equation:
(3√15 x 6√5) / 10√3

Multiply the terms in the numerator:
18√(15 x 5) / 10√3

Simplify:
18√75 / 10√3

Divide both the numerator and denominator by 2:
9√75 / 5√3

Now, simplify further by taking out the common factor under the square roots:
(9 x √25√3) / 5

√25 = 5
(9 x 5 x √3) / 5

45√3 / 5

Finally, divide 45 by 5:
9√3

Therefore, the final answer is:
9√3.