Problem preview

A-REI.2 Warmup M3-013-A12-V02

Solve simple rational and radical equations and identify extraneous solutions.

Solve a simple rational or radical equation by removing the denominator or radical and checking for invalid solutions

Problem

What is the best method for solving this rational or radical equation? \(\sqrt{x+3}=x-1\)

Answer choices

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Isolate the square root, square both sides, solve the resulting equation, and then check the solution in the original equation for any extraneous value.

Isolate the square root and then cube both sides, because cubing is the inverse operation that gets rid of any radical expression.

Square both sides and solve, but there is no need to check the answer afterward because equivalent operations always keep the same solutions.

Clear denominators first by using an LCD, then solve and check restrictions, because rational methods work best whenever x appears in an equation.

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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: Solve a simple rational or radical equation by removing the denominator or radical and checking for invalid solutions