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Advanced MathHardRational equation whose only candidate is excluded

Advanced Math practice question

How many solutions does the equation x/(x + 1) = 3/(x + 1) + 1 have?

  1. A. ZeroCorrect
  2. B. Exactly one
  3. C. Exactly two
  4. D. Infinitely many

Answer: A. Zero

Multiply by (x + 1): x = 3 + (x + 1) → 0 = 4, which is impossible. No value of x works (and x = −1 is excluded anyway).

Why the other answers are wrong

B. Exactly one
Solving loosely gives x = 3 + x + 1, which has no solution, not one.
C. Exactly two
There is no quadratic here.
D. Infinitely many
The equation reduces to a false statement, not an identity.

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