Worksheet: Partial Fraction Decomposition

In this worksheet, we will practice finding the partial fractions of improper rational expressions.

Q1:

Nader wants to convert the rational expression into partial fractions.

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

  • A
  • B
  • C
  • D
  • E

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

  • A
  • B
  • C
  • D
  • E

Q2:

Convert the rational expression 6 𝑥 2 𝑥 + 5 𝑥 + 4 𝑥 + 3 3 2 2 into partial fractions.

  • A 6 𝑥 3 2 ( 𝑥 + 1 ) 1 7 5 2 ( 𝑥 + 3 ) 2 6
  • B 6 𝑥 1 7 5 2 ( 𝑥 + 1 ) + 3 2 ( 𝑥 + 3 ) 2 6
  • C 6 𝑥 3 2 ( 𝑥 + 1 ) + 1 7 5 2 ( 𝑥 + 3 ) + 2 6
  • D 6 𝑥 3 2 ( 𝑥 + 1 ) + 1 7 5 2 ( 𝑥 + 3 ) 2 6
  • E 6 𝑥 + 3 2 ( 𝑥 + 1 ) + 1 7 5 2 ( 𝑥 + 3 ) 2 6

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