Problem preview

A-SSE.1.b Warmup M3-015-A04-V02

Interpret complex polynomial/rational expressions by treating parts as single units.

Find rational domain restrictions from the denominator

Problem

For \((x~+~2)/(x^2~-~9)\), factor the denominator, find its zeros, and state the real-domain exclusions.

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The denominator factors as (x-3)(x+3). Its zeros are x=3 and x=-3, so the domain excludes both values.

The denominator factors as (x-3)(x+3) and has zeros x=3 and x=-3, but no values are excluded.

The denominator factors as (x-3)(x+3), but only x=-3 is excluded from the domain.

The numerator x+2 gives x=-2 as a domain exclusion.

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Curriculum context

Course: Math III
Standard: A-SSE.1.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Interpret complex polynomial/rational expressions by treating parts as single units.
Problem type: Find rational domain restrictions from the denominator