Problem preview

A-APR.7 Warmup M3-007-A06-V04

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

Subtract unlike rational expressions with an LCD and restrictions

Problem

Subtract and fully simplify \((x~+~4)/(x^2~-~16)~-~3/(x~-~4)\) using a least common denominator. State the original restrictions.

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Use LCD (x-4)(x+4): [(x+4)-3(x+4)]/[(x-4)(x+4)]=-2/(x-4), with x≠-4,4.

The difference is -2/(x-4), with x≠4 only.

Add instead to get 4/(x-4).

Use an incorrect denominator (x-4)(x+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: Subtract unlike rational expressions with an LCD and restrictions