32m^4/24m=8*4*m^3*m/8*3m=4*m^3/3

(2m +3)^2 /(4m^3 - 9m)=(2m+3)^2/m(2m+3)(2m-3)=(2m+3)/m*(2m-3)

(sqrt(a)-3)/(a-9)=(sqrt(a)-3)/(sqrt(a)-3)(sqrt(a)+3)=1/sqrt(a)+3