Mississippi Math A3.A.13

MathGrades 9–12Algebra (A) Analyze and Manipulate Functions

The Standard

Write rational expressions in simplest form. (For example (x³ – x² – x + 1)/(x³ + x² – x – 1) = (x–1)/(x+1)).

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Use Polynomials Identities to Solve Problems

Teacher's field guide

What Students Need to Do: Factor the numerator and denominator, then cancel factors common to both. Find the values that make the original denominator zero, even when those factors cancel.
What Mastery Looks Like: For (x²−1)/(x²−x−2), a student gets (x−1)/(x−2) and excludes x=−1 and x=2. They can check the result by substituting an allowed value into both expressions.
Common Misconceptions: Students may cancel x from x+1 and x+2, even though x is not a factor of either expression. They may also allow a value that made the original denominator zero because its factor canceled.
How to Assess It: Give an exit ticket: Simplify (x²+3x+2)/(x²+4x+3) and list every excluded value. Ask students to circle the factor they canceled.

Lesson moves

Give pairs two x+1 cards, one x+2 card, and one x+3 card to factor (x²+3x+2)/(x²+4x+3), cancel, and record exclusions.
Ask: Why does (x+1)/(x+1) equal 1 at x=2 but have no value at x=−1?
Run a card match: students order (x²−1)/(x²+2x+1), (x−1)(x+1)/(x+1)², (x−1)/(x+1), and the restriction x≠−1.
A shop spends n²+5n dollars to make n shirts; have students simplify the cost per shirt and explain why n=0 is excluded.

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