Use this rule when dividing fractions:
#color(red)a/color(blue)bdivcolor(green)c/color(purple)dqquad=>qquadcolor(red)a/color(blue)bxxcolor(purple)d/color(green)c#
And use this rule to combine them:
#color(red)a/color(blue)bxxcolor(purple)d/color(green)cqquad=>qquad(color(red)axxcolor(purple)d)/(color(blue)bxxcolor(green)c#
Now here's our problem:
#color(white)=color(red)(5a)/color(blue)(12bc^2)divcolor(green)(15a^2)/color(purple)(18b^2c^2)#
#=color(red)(5a)/color(blue)(12bc^2)xxcolor(purple)(18b^2c^2)/color(green)(15a^2)#
#=(color(red)(5a)xxcolor(purple)(18b^2c^2))/(color(blue)(12bc^2)xxcolor(green)(15a^2))#
#=(color(purple)(color(magenta)90color(red)ab^2c^2))/(color(blue)(12bc^2)xxcolor(green)(15a^2))#
#=(color(purple)(color(magenta)90color(red)ab^2c^2))/color(blue)(color(turquoise)180color(green)(a^2)bc^2)#
#=(color(purple)(color(red)cancelcolor(magenta)90^color(black)1color(red)ab^2c^2))/color(blue)(color(red)cancelcolor(turquoise)180^color(black)2color(green)(a^2)bc^2)#
#=(color(purple)(color(red)ab^2c^2))/color(blue)(color(black)2color(green)(a^2)bc^2)#
#=(color(purple)(color(red)ab^2color(red)cancelcolor(blue)(c^2)))/color(blue)(color(black)2color(green)(a^2)bcolor(red)cancelcolor(blue)(c^2))#
#=(color(purple)(color(red)ab^2))/color(blue)(color(black)2color(green)(a^2)b)#
#=(color(purple)(color(red)ab^color(red)cancelcolor(purple)2))/color(blue)(color(black)2color(green)(a^2)color(red)cancelcolor(blue)b)#
#=(color(purple)(color(red)ab))/color(blue)(color(black)2color(green)(a^2))#
#=(color(purple)(color(red)color(black)cancelcolor(red)ab))/color(blue)(color(black)2color(green)(a^color(red)cancelcolor(green)2))#
#=color(purple)b/(color(black)2color(green)a)#
This is the simplified result. Hope this helped!