Question 31529
First step is to find the common denominators of both the numerator and denominator:
(25x^2-9y^2)/xy/(5/y-3/x)

Numerator LCD: xy
Denominator LCD: xy

Whatever is missing needs to multiplied:
The xy is missing below the 25x^2 in the numerator
The x is missing below the 5 and the y is missing below the 3 so multiply them to the numerator

Above shown:
((25x^2(xy)/xy)-9y^2/xy)/(5(x)/xy-3(y)/xy)

Combine and Simplify
(25x^3y-9y^2/xy)/(5x-3y/xy)

Divide:
(25x^3y-9y^2/xy)(xy/5x-3y)

The xy's cross cancel to simplify to:
25x^3y-9y^2/5x-3y

One last factoring:
y(25x^3-9y)/5x-3y

Note: The difference of two square rules doesn't apply here because both of the quantities don't have powers of two.