If 1/x + 1/y = 3 and 1/x - 1/y = 7, what is the value of x + y? Express your answer as a common fraction.
1/x + 1/y = 3
1/x - 1/y = 7 add these equations
2/x = 10
2/10 = x = 1/5
So
1 / (1/5) + 1/y = 3
5 + 1/y = 3
1/y = 3 - 5
1/y = -2
-1/2 = y
x + y =
1/5 - 1/2 =
2/10 - 5/10 =
-3 / 10
