We can let a = 1/(x-1) b = 1/(y+2) and rewrite the equations as 2a - b = 10 a + 3b = -9 Using the first to write an expression for b, we get b = 2a - 10 Substituting this into the second equation gives a + 3(2a -10) = -9 7a -30 = -9 . . . . . . . . simplify 7a = 21 . . . . . . . . . . .add 30 a = 3 b = 2·3 - 10 = -4
Now, we can find x and y. 3 = 1/(x -1) x - 1 = 1/3 x = 1 1/3 = 4/3
-4 = 1/(y +2) y +2 = -1/4 y = -2 1/4 = -9/4
Then the desired sum is x + y = 4/3 -9/4 = (16 -27)/12 x + y = -11/12
