Worksheet: Partial Fractions: Nonrepeated Irreducible Quadratic Factors

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In this worksheet, we will practice decomposing rational expressions into partial fractions when the denominator has nonrepeated irreducible quadratic factors.

Q1:

Express 3𝑥+1(𝑥+4)(𝑥−3) in partial fractions.

  • A21𝑥−67169(𝑥+4)−21169(𝑥−3)+1013(𝑥−3)
  • B21𝑥−67169(𝑥+4)+1013(𝑥−3)
  • C21𝑥−67169(𝑥+4)+21169(𝑥−3)+1013(𝑥−3)
  • D21𝑥−67169(𝑥+4)−10169(𝑥−3)+2113(𝑥−3)
  • E21𝑥−67169(𝑥+4)+10169(𝑥−3)+2113(𝑥−3)

Q2:

The expression 3𝑥−2(𝑥+4)(𝑥−3) can be written in the form 𝐴𝑥+𝐵𝑥+4+𝐶𝑥−3. Find the values of 𝐴, 𝐵, and 𝐶.

  • A𝐴=113, 𝐵=1013, 𝐶=113
  • B𝐴=−713, 𝐵=1813, 𝐶=713
  • C𝐴=−113, 𝐵=1013, 𝐶=113
  • D𝐴=−713, 𝐵=1013, 𝐶=713
  • E𝐴=1813, 𝐵=−713, 𝐶=113

Q3:

Express 𝑥−3(𝑥+2)(𝑥−1) in partial fractions.

  • A𝑥+13(𝑥+2)−13(𝑥−1)
  • B23(𝑥+2)−5𝑥+53(𝑥−1)
  • C5𝑥+53(𝑥+2)−23(𝑥−1)
  • D5𝑥+13(𝑥+2)−23(𝑥−1)
  • E5𝑥+53(𝑥+2)−13(𝑥−1)

Q4:

Decompose the following to partial fractions: 𝑥+1𝑥+8.

  • A4−7𝑥12(𝑥+2𝑥−4)+512(𝑥+2)
  • B7𝑥−412(𝑥+2𝑥−4)+512(𝑥+2)
  • C4−7𝑥12(𝑥−2𝑥+4)+512(𝑥+2)
  • D7𝑥−412(𝑥−2𝑥+4)+512(𝑥+2)
  • E7𝑥−4(𝑥−2𝑥+4)+5(𝑥+2)

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