-1/12
1) Evaluating that expression we can write
[tex]\frac{1}{2}+(-\frac{5}{6})+\frac{1}{4}[/tex]
2) We need to find out a common denominator for those. Let's calculate the LCM by factoring by prime numbers:
[tex]\begin{gathered} \frac{(12\colon2\times1)-(12\colon6\times5)+(12\colon4\times1)}{12} \\ \frac{6-10+3}{12}=-\frac{1}{12} \end{gathered}[/tex]
Note that when reducing to a common denominator, we have divided 12 by each original denominator and multiplied by its original numerator. In other words:
[tex]\begin{gathered} \\ \frac{1}{2}+(-\frac{5}{6})+\frac{1}{4}=\frac{6-10+3}{12}=-\frac{1}{12} \end{gathered}[/tex]
3) Hence the answer is -1/12
