For \(1/(x~-~1)~+~x~=~3\), state the restriction, check the repeated candidate in the original equation, and report the valid real root to the nearest hundredth.

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Restriction: none. Check: the repeated candidate x=2 passes the original equation. Valid root to the nearest hundredth: 2.00.

Restriction: x≠1. Check: treat the excluded value x=1 as the repeated candidate. Valid root to the nearest hundredth: 1.00.

Restriction: x≠1. Check: skip the original-equation check. Valid root without the requested rounding or tolerance: 2.

Restriction: x≠1. Check: the repeated candidate x=2 passes the original equation. Valid root to the nearest hundredth: 2.00.

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Curriculum context

Course: Math III
Standard: A-REI.2
Category: Algebra
Domain: Reasoning with Equations and Inequalities
Objective: Solve simple rational and radical equations and identify extraneous solutions.
Problem type: Approximate every valid real root with restrictions and tolerance