Problem preview

A-APR.7 Warmup M3-007-A02-V03

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 \([(x~+~2)/(x~-~3)]\) by \([(x~+~2)/(x~+~1)]\). State the restrictions from the original denominators and from the divisor being nonzero.

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Do not take the reciprocal, giving (x+2)²/[(x-3)(x+1)].

The quotient is (x+1)/(x-3), but omit the zero-divisor exclusion x≠-2.

The quotient is (x+1)/(x-3), with x≠-1,3 only.

Multiply by the reciprocal and cancel to get (x+1)/(x-3), with x≠-2,-1,3.

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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