Express (5sqrt(3)-6)/(2sqrt(3)+3) in the form m+nsqrt(3) where m and n are integers. [Core 1]

Step 1: multiply (5sqrt(3)-6)/(2sqrt(3)+3) by (2sqrt(3)-3)/(2sqrt(3)-3) (this is a trick called CONJUGATION as you're really just multiplying the fraction by 1. Step 2: Expand and simplify top and botton to arrive at: (48-27sqrt(3))/3 Step 3: cancel top and bottom with the "3". Step 4: arrive at 16-9sqrt(3). m=16,n=-9.