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Worksheet: Partial Fraction Decomposition

Q1:

Convert the rational expression 6 π‘₯ βˆ’ 2 π‘₯ + 5 π‘₯ + 4 π‘₯ + 3 3 2 2 into partial fractions.

  • A 6 π‘₯ βˆ’ 3 2 ( π‘₯ + 1 ) βˆ’ 1 7 5 2 ( π‘₯ + 3 ) βˆ’ 2 6
  • B 6 π‘₯ βˆ’ 1 7 5 2 ( π‘₯ + 1 ) + 3 2 ( π‘₯ + 3 ) βˆ’ 2 6
  • C 6 π‘₯ βˆ’ 3 2 ( π‘₯ + 1 ) + 1 7 5 2 ( π‘₯ + 3 ) + 2 6
  • D 6 π‘₯ βˆ’ 3 2 ( π‘₯ + 1 ) + 1 7 5 2 ( π‘₯ + 3 ) βˆ’ 2 6
  • E 6 π‘₯ + 3 2 ( π‘₯ + 1 ) + 1 7 5 2 ( π‘₯ + 3 ) βˆ’ 2 6

Q2:

Mason wants to convert the rational expression 6 π‘₯ + 5 π‘₯ βˆ’ 4 5 π‘₯ + 6 π‘₯ 2 2 into partial fractions.

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

  • A 6 5 βˆ’ 2 5 π‘₯ + 3 0 π‘₯ 1 1 π‘₯ + 2 0 2
  • B 6 5 βˆ’ 1 1 π‘₯ βˆ’ 2 0 2 5 π‘₯ + 3 0 π‘₯ 2
  • C 6 5 βˆ’ 1 1 5 π‘₯ + 4
  • D 6 5 βˆ’ 1 1 π‘₯ + 2 0 2 5 π‘₯ + 3 0 π‘₯ 2
  • E 6 5 + 1 1 π‘₯ + 2 0 2 5 π‘₯ + 3 0 π‘₯ 2

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

  • A 6 5 + 1 7 1 5 ( 5 π‘₯ + 6 ) βˆ’ 2 3 π‘₯
  • B 5 6 + 1 7 2 2 ( 2 π‘₯ βˆ’ 1 ) βˆ’ 8 3 3 ( 3 π‘₯ + 4 )
  • C 6 5 + 1 7 1 5 ( 5 π‘₯ + 6 ) + 2 3 π‘₯
  • D 6 5 βˆ’ 1 7 1 5 ( 5 π‘₯ + 6 ) + 2 3 π‘₯
  • E 6 5 βˆ’ 8 3 1 5 ( 5 π‘₯ + 6 ) + 2 3 π‘₯