Problem preview

A-APR.7 Warmup M3-007-A07-V04

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

Simplify a complex rational expression with all restriction sources

Problem

Simplify \([(x^2~-~4)/(x^2~-~1)]/[(x~-~2)/(x~+~1)]\) and state its complete original domain.

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The expression is (x+2)/(x-1), with x≠-1,1 only.

Cancel without taking the reciprocal to get (x+2)/(x+1).

Do not take the reciprocal, giving (x-2)²(x+2)/[(x-1)(x+1)²].

Factor, multiply by the reciprocal, and cancel x-2 and x+1 to get (x+2)/(x-1), with x≠-1,1,2.

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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: Simplify a complex rational expression with all restriction sources