A way to add fractions that always works is to multiply each numerator by the denominator of the other, then express the sum of products over the product of the denominators.
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{a}{b}\cdot\dfrac{d}{d}+\dfrac{c}{d}\cdot\dfrac{b}{b}\\\\=\dfrac{ad+bc}{bd}[/tex]
Here, you have
[tex]\dfrac{-5}{4}-\dfrac{-1}{6}=\dfrac{-5\cdot6-(-1)\cdot4}{4\cdot6}=\dfrac{-26}{24}\\\\=\dfrac{-13}{12}=-1\frac{1}{12}[/tex]
The sum is -1 1/12
