Partial Fraction Decomposition Worksheet

Grade 12 Math worksheet on partial fraction decomposition, covering various cases and problem types.

Grade 12 Math AlgebraPartial Fraction Decomposition

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Includes

4 Short AnswerMultiple Choice

Standards

CCSS.MATH.CONTENT.HS.APR.D.6CCSS.MATH.CONTENT.HS.APR.D.7

Topics

AlgebraPre-calculusPartial FractionsDecomposition

7 sections · Free to use · Printable

Partial Fraction Decomposition

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Decompose each rational expression into its partial fractions. Show all your work.

1. Decompose the following rational expression:

(5x - 1) / (x² - 1)

2. Decompose the following rational expression:

(4x) / ((x - 2)²)

3. Decompose the following rational expression:

(x - 3) / (x(x² + 1))

4. First, perform long division, then decompose the resulting proper rational expression:

(x³ + x² + x + 1) / (x² + x)

5. Which of the following is the correct partial fraction decomposition of (2x + 3) / (x² + 3x + 2)?

A/(x+1) + B/(x+2)

2/(x+1) - 1/(x+2)

1/(x+1) + 1/(x+2)

1/(x+1) + 2/(x+2)

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