Interpret complex polynomial/rational expressions by treating parts as single units.
Build the real domain of a nested radical or rational expression
Problem
Find the real domain of \(\sqrt{(x~+~1)/(x~-~2)}\). State the radicand condition, denominator exclusion, and resulting intervals.
Big Picture
What this problem is really about
Nested expressions impose restrictions from the inside out. First preserve the inner denominator’s exclusion; then require the entire quotient under the square root to be nonnegative, since a numerator radical may equal zero. A sign chart combines both conditions, with a numerator zero potentially included and a denominator zero always excluded.
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