First we need to convert the two mixed numbers into improper fractions:

#1 1/2 -: 1 4/5 => (1 + 1/2) -: (1 + 4/5) =>#

#([2/2 xx 1] + 1/2) -: ([5/5 xx 1] + 4/5) =>#

#(2/2 + 1/2) -: (5/5 + 4/5) =>#

#3/2 -: 9/5#

We can next rewrite this expression as:

#3/2 -: 9/5 => (3/2)/(9/5)#

We can now use this rule for dividing fractions to evaluate the expression:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

#(color(red)(3)/color(blue)(2))/(color(green)(9)/color(purple)(5)) => (color(red)(3) xx color(purple)(5))/(color(blue)(2) xx color(green)(9)) => (cancel(color(red)(3)) xx color(purple)(5))/(color(blue)(2) xx cancel(color(green)(9))3) =>#

#5/6#