Worksheet: Partial Fractions: Nonrepeated Linear Factors

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


Express 𝑥2(𝑥+2)(𝑥3)(𝑥+1) in partial fractions.

  • A14(𝑥+1)+25(𝑥+2)+720(𝑥3)
  • B14(𝑥+1)+2(𝑥+2)+720(𝑥3)
  • C12(𝑥+1)+25(𝑥+2)+720(𝑥3)
  • D12(𝑥+1)+15(𝑥+2)+720(𝑥3)
  • E14(𝑥+1)+25(𝑥+2)+14(𝑥3)


Find 𝐴 and 𝐵 such that 4𝑥2(𝑥+3)(𝑥2)=𝐴𝑥+3+𝐵𝑥2.

  • A𝐴=145, 𝐵=65
  • B𝐴=65, 𝐵=145
  • C𝐴=145, 𝐵=65
  • D𝐴=145, 𝐵=65
  • E𝐴=65, 𝐵=145


Express 𝑥2𝑥(𝑥3) in partial fractions.

  • A23𝑥+1(𝑥3)
  • B2𝑥+13(𝑥3)
  • C2𝑥+1(𝑥3)
  • D13𝑥+23(𝑥3)
  • E23𝑥+13(𝑥3)


The expression 2𝑥+1(𝑥+2)(𝑥+3) can be written in the form 𝐴𝑥+3+𝐵𝑥+2. Find the values of 𝐴 and 𝐵.

  • A𝐴=5,𝐵=3
  • B𝐴=3,𝐵=5
  • C𝐴=5,𝐵=3
  • D𝐴=5,𝐵=3
  • E𝐴=5,𝐵=3


Find 𝐴 and 𝐵 such that 4(𝑥+8)(𝑥2)=𝐴𝑥2+𝐵𝑥+8.

  • A𝐴=25, 𝐵=25
  • B𝐴=25, 𝐵=25
  • C𝐴=25, 𝐵=25
  • D𝐴=15, 𝐵=15
  • E𝐴=25, 𝐵=25


Mason wants to convert the rational expression 6𝑥+5𝑥45𝑥+6𝑥 into partial fractions.

His first step is to divide the numerator by the denominator. Complete this division.

  • A6511𝑥2025𝑥+30𝑥
  • B65+11𝑥+2025𝑥+30𝑥
  • C6511𝑥+2025𝑥+30𝑥
  • D6525𝑥+30𝑥11𝑥+20
  • E65115𝑥+4

Mason now converts this expression into partial fractions. Convert the expression into partial fractions.

  • A65+1715(5𝑥+6)+23𝑥
  • B658315(5𝑥+6)+23𝑥
  • C56+1722(2𝑥1)833(3𝑥+4)
  • D651715(5𝑥+6)+23𝑥
  • E65+1715(5𝑥+6)23𝑥


Convert the rational expression 6𝑥2𝑥+5𝑥+4𝑥+3 into partial fractions.

  • A6𝑥+32(𝑥+1)+1752(𝑥+3)26
  • B6𝑥1752(𝑥+1)+32(𝑥+3)26
  • C6𝑥32(𝑥+1)+1752(𝑥+3)+26
  • D6𝑥32(𝑥+1)1752(𝑥+3)26
  • E6𝑥32(𝑥+1)+1752(𝑥+3)26

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