(x + y + 1) / (x - y - 1) = 2
(x + y - 1) / (x - y - 1) = -1
multiply both sides by x - y - 1
x + y + 1 = 2(x - y - 1)
x + y - 1 = -1(x - y - 1)
expand and simplify
x + y + 1 = 2x - 2y - 2
x + y - 1 = -x + y + 1
.
-x + 3y = -3
2x + 0y = 2
second equation: 2x = 2, so x = 1
first equation: -1 + 3y = -3
3y = -2
y = -2/3
.
Important! Since we have a fraction, we need to check if our answer makes the bottom zero.
x - y - 1
1 - (-2/3) - 1
1 + 2/3 - 1
2/3
The answer does not make the bottom of the fraction zero, so we're allowed to use that answer.
Answer: x = 1, y = -2/3