First, let's deal with the multiplication within the parenthesis on the right:
#(1/2 + (2/3 -: 3/4) - (4/5 * 5/6)) ->#
#(1/2 + (2/3 -: 3/4) - (4/color(red)(cancel(color(black)(5))) * color(red)(cancel(color(black)(5)))/6)) ->#
#(1/2 + (2/3 -: 3/4) - (4/6)) ->#
#(1/2 + (2/3 -: 3/4) - ((2 xx 2)/(2 xx 3))) ->#
#(1/2 + (2/3 -: 3/4) - ((color(red)(cancel(color(black)(2))) xx 2)/(color(red)(cancel(color(black)(2))) xx 3))) ->#
#(1/2 + (2/3 -: 3/4) - 2/3)#
Now, we can rewrite the division term as:
#(1/2 + ((2/3)/(3/4)) - 2/3)#
And then use the rule for dividing fractions:
#(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))#
#(1/2 + ((2 xx 4)/(3 xx 3)) - 2/3)#
#(1/2 + 8/9 - 2/3)#
Now we can multiply each fraction by the appropriate form of #1# to get each fraction over a common denominator, in this case #18#
#((1/2 xx 9/9) + (8/9 xx 2/2) - (2/3 xx 6/6))#
#9/18 + 16/18 - 12/18#
#(9 + 16 - 12)/18#
#(25 - 12)18#
#13/18#
