Problem preview

A-APR.7 Warmup M3-007-A02-V04

Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.

Divide rational expressions with denominator and zero-divisor restrictions

Problem

Divide and fully simplify \([(x^2~-~4)/(x^2~-~x~-~6)]\) by \([(x~-~2)/(x~-~3)]\). State the restrictions from the original denominators and from the divisor being nonzero.

Answer choices

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Do not take the reciprocal, giving (x-2)²/(x-3)².

The quotient is 1, with x≠-2,3 only.

Factor, multiply by the reciprocal, and cancel to get 1, with x≠-2,2,3.

The quotient is 1, but omit the zero-divisor exclusion x≠2.

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Curriculum context

Course: Math III
Standard: A-APR.7
Category: Algebra
Domain: Arithmetic with Polynomials and Rational Expressions
Objective: Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Problem type: Divide rational expressions with denominator and zero-divisor restrictions