Originally Posted by

**ebaines** This is simple manipulation of fractions.

$\displaystyle \frac {-1}{-3} + \frac 1 {-5} = \frac 1 3 + \frac {-1} 5 $

To add these two fractions with different denominators you have to find the smallest common multiple of 3 and 5, which is 15. So:

$\displaystyle \frac 1 3 = \frac {1 \times 5}{3 \times 5} = \frac 5 {15} $

$\displaystyle \frac {-1} 5 = \frac {-1 \times 3}{5 \times 3 } = \frac {-3} {15} $

Hence:

$\displaystyle \frac 1 3 + \frac{-1 } 5 = \frac 5 {15} + \frac {-3} {15} = \frac 2 {15}$