Mississippi Math A3.A.14
The Standard
Decompose a rational function into partial fractions.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Use Polynomials Identities to Solve Problems
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students factor the denominator and rewrite one rational expression as a sum of simpler fractions. They find the missing numerators by clearing denominators and matching coefficients. If the fraction is improper, they divide first.
What Mastery Looks Like
- A student can rewrite (3x+5)/((x+1)(x+2)) as 2/(x+1)+1/(x+2), then check by combining the fractions. For a factor (x+1)², they include terms over both x+1 and (x+1)².
Common Misconceptions
- Students may put the original numerator over each factor instead of finding new numerators. They may skip division when the numerator's degree is too high or leave out a term for a repeated factor.
How to Assess It
- Exit ticket: Decompose (5x+7)/((x+1)(x+2)). Combine your fractions to check the result.
Lesson moves
Ways to Teach It
Give pairs cards with rational expressions and two-term decompositions; have them match the cards and check each match by combining fractions.
Ask partners to explain why A/(x+1)+B/(x+2) does not have A+B as its numerator when combined.
Run a two-minute coefficient race using (4x+7)/((x+1)(x+2)); teams find both numerators and verify their answers.
Two pumps have a combined rate (3t+5)/((t+1)(t+2)) liters per minute; find each pump's rate, a/(t+1) and b/(t+2).
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Printable A3.A.14 Worksheet
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