Problem preview

A-SSE.2 Warmup M3-016-A14-V04

Use expression structure to find useful rewrites.

Decide whether a rewrite changes the domain and identify which restrictions must still be preserved

Problem

Does rewriting \(\sqrt{(x+2)/(x-1)}\) as \(\sqrt{x+2}/\sqrt{x-1}\) change the domain?

Answer choices

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Yes. The original allows x<=-2 or x>1, but the rewrite sqrt(x+2)/sqrt(x-1) requires x>1.

Yes. The rewrite adds x<=-2 as a new allowed interval.

No. Both expressions have domain x>1.

No. Both expressions have domain x<=-2 or x>1.

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Curriculum context

Course: Math III
Standard: A-SSE.2
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Use expression structure to find useful rewrites.
Problem type: Decide whether a rewrite changes the domain and identify which restrictions must still be preserved