The given expression is
[tex]|(\frac{1}{4}-\frac{1}{5})+(-\frac{3}{4}+\frac{1}{8})|[/tex]First, less solve each difference of fractions.
[tex]|\frac{1}{4}-\frac{1}{5}-\frac{3}{4}+\frac{1}{8}|[/tex]Now, we find the least common multiple.
4 5 4 8 | 2
2 5 2 4 | 2
1 5 1 2 | 2
1 5 1 1 | 5
1 1 1 1
So, the least common factor is 2x2x2x5=40
[tex]|\frac{10-8-30+5}{40}|=|\frac{-23}{40}|=\frac{23}{40}[/tex]