x+y = 19
x - y = 5
2x = 24
x = 12
12 - y = 5
y = 7
If the sum of two numbers is 19 and the difference of those two numbers is 5, then the numbers are 12 and 7.
As far as the fraction in lowest terms, you haven't told what the fraction is to begin with- (what)/(what else)