domain restriction

A domain restriction is a rule that fences off certain inputs as not allowed. The domain of an expression is the full set of inputs you may legally feed it; a restriction is any place where some operation would break down, carving a hole in that set.

Three operations commonly trigger restrictions: division (you may not divide by zero), even roots (you may not take the square root of a negative number and stay real), and logarithms (you may not take the log of zero or a negative). For rational expressions only the first matters, so every restriction comes from a denominator that could be zero.

Stating a restriction is part of giving a complete, honest answer. Writing (x + 2)/(x - 1) = something “for x ≠ 1” is more truthful than leaving the condition unsaid, because the equation simply has no meaning at x = 1. The restriction is not a nuisance — it is the boundary inside which everything you wrote is actually valid.