Turn the second fraction over, as with multiplying numerical fractions. For example, let's look at [3x(x+8)/x^2-x] / [3x-9/x-1]. Flip the second fraction over, so you have [3x(x+8)/x^2-x] * [x-1/3x-9].
Multiply numerator by numerator, and denominator by denominator. Now you have 3x(x+8)(x-1)/(x^2-x)(3x-9).
Simplify where possible. That gives you 3x(x+8)(x-1)/3x(x-1)(x-3). Cancel out the 3x and the (x-1), and you have x+8/x-3.