Multiplying fractions is as simple as multiplying numerators together and denominators together to form a new fraction (which may still need to be reduced to its lowest form)
Dividing fractions is done by inverting the numerator and denominator of the right hand side fraction, and then changing the division into a multiplication (as above)
So, assuming . means multiply (and noting there are no divisions in your example)
1/2+(2/3+3/4)-(4/5·5/6)=?
So the additions
1/2+(2/3+3/4) = (6+8+9)12 = 23/12 = 1 11/12
and the multiplcation
4/5 x 5/6
=(4 x 5)/(5 x 6)
=20/30
=2/3
The subtraction
1 11/12 - 2/3
=23/12 - 8/12
= 15/12
= 5/4
=1 1/4
Check your answers here:
http://statsfiddle.info/Fraction/FractionArithmetic?w1=0&n1=4&d1=5&op=Times&w2=0&n2=5&d2=6