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Worksheet: Simplifying Complex Fractions Involving Polynomials

Q1:

Simplify the function 𝑛 ( π‘₯ ) = 7 π‘₯ + π‘₯ + 6 3 π‘₯ + 6 9 π‘₯ + 6 , and find its domain in ℝ .

  • A 𝑛 ( π‘₯ ) = 7 , domain = ℝ
  • B 𝑛 ( π‘₯ ) = 7 , domain = ℝ βˆ’ { βˆ’ 6 }
  • C 𝑛 ( π‘₯ ) = 1 7 , domain = ℝ βˆ’ { βˆ’ 6 , βˆ’ 3 }
  • D 𝑛 ( π‘₯ ) = 7 , domain = ℝ βˆ’ { βˆ’ 6 , βˆ’ 3 }
  • E 𝑛 ( π‘₯ ) = 1 7 , domain = ℝ βˆ’ { βˆ’ 6 }

Q2:

Simplify the function 𝑛 ( π‘₯ ) = 2 π‘₯ + 3 π‘₯ + 9 8 π‘₯ + 1 4 1 4 7 π‘₯ + 1 4 , and find its domain in ℝ .

  • A 𝑛 ( π‘₯ ) = 2 3 , domain = ℝ
  • B 𝑛 ( π‘₯ ) = 2 3 , domain = ℝ βˆ’ { βˆ’ 1 4 }
  • C 𝑛 ( π‘₯ ) = 3 2 , domain = ℝ βˆ’ { βˆ’ 1 4 , βˆ’ 7 }
  • D 𝑛 ( π‘₯ ) = 2 3 , domain = ℝ βˆ’ { βˆ’ 1 4 , βˆ’ 7 }
  • E 𝑛 ( π‘₯ ) = 3 2 , domain = ℝ βˆ’ { βˆ’ 1 4 }

Q3:

Simplify the function 𝑛 ( π‘₯ ) = 6 π‘₯ + 3 π‘₯ + 1 5 0 π‘₯ βˆ’ 1 0 7 5 π‘₯ βˆ’ 1 0 , and find its domain in ℝ .

  • A 𝑛 ( π‘₯ ) = 2 , domain = ℝ
  • B 𝑛 ( π‘₯ ) = 2 , domain = ℝ βˆ’ { 1 0 }
  • C 𝑛 ( π‘₯ ) = 1 2 , domain = ℝ βˆ’ { 5 , 1 0 }
  • D 𝑛 ( π‘₯ ) = 2 , domain = ℝ βˆ’ { 5 , 1 0 }
  • E 𝑛 ( π‘₯ ) = 1 2 , domain = ℝ βˆ’ { 1 0 }

Q4:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ + 4 π‘₯ + 4 9 π‘₯ βˆ’ 1 4 1 9 6 π‘₯ βˆ’ 1 4 , and find its domain in ℝ .

  • A 𝑛 ( π‘₯ ) = 1 4 , domain = ℝ
  • B 𝑛 ( π‘₯ ) = 1 4 , domain = ℝ βˆ’ { 1 4 }
  • C 𝑛 ( π‘₯ ) = 4 , domain = ℝ βˆ’ { 7 , 1 4 }
  • D 𝑛 ( π‘₯ ) = 1 4 , domain = ℝ βˆ’ { 7 , 1 4 }
  • E 𝑛 ( π‘₯ ) = 4 , domain = ℝ βˆ’ { 1 4 }

Q5:

Simplify 3 + 1 βˆ’ 1 5 π‘₯ 2 5 π‘₯ 2 completely.

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