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Worksheet: Factoring Algebraic Fractions

Q1:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ + 7 π‘₯ 6 π‘₯ + 2 5 π‘₯ + 4 Γ· 6 π‘₯ βˆ’ π‘₯ 3 6 π‘₯ βˆ’ 1 2 2 2 2 .

  • A 𝑛 ( π‘₯ ) = π‘₯ + 7 π‘₯ βˆ’ 4
  • B 𝑛 ( π‘₯ ) = π‘₯ + 4 π‘₯ + 7
  • C 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 4 π‘₯ + 7
  • D 𝑛 ( π‘₯ ) = π‘₯ + 7 π‘₯ + 4
  • E 𝑛 ( π‘₯ ) = π‘₯ + 7 π‘₯ π‘₯ + 4 π‘₯ 2 2

Q2:

Simplify the function 𝑛 ( π‘₯ ) = 9 π‘₯ + 7 2 π‘₯ + 1 Γ· 9 π‘₯ + 7 2 5 π‘₯ + 5 .

  • A 𝑛 ( π‘₯ ) = 8 1 5
  • B 𝑛 ( π‘₯ ) = 1 5
  • C 𝑛 ( π‘₯ ) = 5 8 1
  • D 𝑛 ( π‘₯ ) = 5

Q3:

Simplify the function 𝑛 ( π‘₯ ) = 5 π‘₯ + 1 5 π‘₯ + 5 Γ· 6 π‘₯ + 1 8 4 π‘₯ + 2 0 .

  • A 𝑛 ( π‘₯ ) = 1 5 2
  • B 𝑛 ( π‘₯ ) = 3 1 0
  • C 𝑛 ( π‘₯ ) = 2 1 5
  • D 𝑛 ( π‘₯ ) = 1 0 3
  • E 𝑛 ( π‘₯ ) = 5 2 4

Q4:

Which of the following functions are equal?

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q5:

Given that 8 𝑦 𝑦 + 2 𝑦 βˆ’ 9 𝑦 𝑦 + 2 𝑦 = βˆ’ 2 2 3 2 2 , find the value of 𝑦 .

  • A0
  • B 5 2
  • C4
  • D βˆ’ 3 2

Q6:

Which of the following functions are equal?

  • A 𝑛 ( π‘₯ ) = π‘₯ + 8 π‘₯ 1 , 𝑛 ( π‘₯ ) = ( π‘₯ + 8 ) ( π‘₯ + 2 1 ) π‘₯ ( π‘₯ + 2 1 ) 2
  • B 𝑛 ( π‘₯ ) = π‘₯ + 8 π‘₯ 1 , 𝑛 ( π‘₯ ) = ( π‘₯ + 8 ) ο€Ή π‘₯ βˆ’ 2 1  π‘₯ ( π‘₯ βˆ’ 2 1 ) 2 2 2
  • C 𝑛 ( π‘₯ ) = π‘₯ + 8 π‘₯ 1 , 𝑛 ( π‘₯ ) = ( π‘₯ + 8 ) ( π‘₯ + 2 1 ) π‘₯ ( π‘₯ + 2 1 ) 2 2
  • D 𝑛 ( π‘₯ ) = π‘₯ + 8 π‘₯ 1 , 𝑛 ( π‘₯ ) = ( π‘₯ + 8 ) ο€Ή π‘₯ + 2 1  π‘₯ ( π‘₯ + 2 1 ) 2 2 2
  • E 𝑛 ( π‘₯ ) = π‘₯ + 8 π‘₯ 1 , 𝑛 ( π‘₯ ) = ( π‘₯ + 8 ) ( π‘₯ βˆ’ 2 1 ) π‘₯ ( π‘₯ βˆ’ 2 1 ) 2

Q7:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ + 4 π‘₯ βˆ’ 1 2 π‘₯ βˆ’ 3 6 Γ· 5 π‘₯ βˆ’ 1 0 π‘₯ βˆ’ 1 2 π‘₯ + 3 6 2 2 2 .

  • A 𝑛 ( π‘₯ ) = 5 π‘₯ βˆ’ 6
  • B 𝑛 ( π‘₯ ) = π‘₯ + 6 5
  • C 𝑛 ( π‘₯ ) = 5 π‘₯ + 6
  • D 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 6 5
  • E 𝑛 ( π‘₯ ) = 1 5 ( π‘₯ βˆ’ 6 )

Q8:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 1 3 π‘₯ + 4 0 π‘₯ βˆ’ 6 4 Γ· 9 π‘₯ βˆ’ 4 5 π‘₯ + 1 6 π‘₯ + 6 4 2 2 2 .

  • A 𝑛 ( π‘₯ ) = 9 π‘₯ + 8
  • B 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 8 9
  • C 𝑛 ( π‘₯ ) = 9 π‘₯ βˆ’ 8
  • D 𝑛 ( π‘₯ ) = π‘₯ + 8 9
  • E 𝑛 ( π‘₯ ) = 1 9 ( π‘₯ + 8 )