Can anyone solve this algebra problem?

Question

Solve for u,v:

(1/ u + v - 1) + (1/ u + v + 1) = 0

Answer 1

values for u and v cannot be determined because you only have one equation of two variables.

however, the relationship between u and v is:

(1/ u + v - 1) + (1/ u + v + 1) = 0
1/u + 1/u + v + v -1 + 1 = 0
2/u + 2v = 0
1/u + v = 0
1 + uv = 0
uv = -1
u = -1/v

Answer 2

yes, someone can.

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Oh. You meant, can we do it and show how?

(1/ u + v - 1) + (1/ u + v + 1) = 0

(1/ u + uv/u - u/u) + (1/ u + uv + u/u) = 0
(1 + uv -u)/u + (1 + uv + u)/u = 0

multiply both sides by u
(1 + uv -u) + (1 + uv + u) = 0
2 + 2 uv = 0
2 uv = -2
uv = -1

(since you have two unknows and only one equation, the best we can do is this curve. The equation can be anywhere along this line.

e.g., u = 1 and v = -1

CHECK
(1/ u + v - 1) + (1/ u + v + 1) = 0
(1/1 -1 -1) + (1/1 -1 + 1) = 0
(-1) + (+1) = 0
TRUE