Problem preview

A-APR.7 Warmup M3-007-A04-V04

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

Subtract rational expressions over a common denominator with restrictions

Problem

Subtract and fully simplify \((x~+~2)/(x^2~-~1)~-~3/(x^2~-~1)\). State the original restrictions.

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

Subtract the denominators to get 0, so the expression is undefined.

Add the numerators to get (x+5)/[(x-1)(x+1)].

The numerator is x+2-3=x-1. Cancel x-1 from (x-1)(x+1) to get 1/(x+1), with x≠-1,1.

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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: Subtract rational expressions over a common denominator with restrictions