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Worksheet: Adding and Subtracting Rational Expressions with Like Denominators

Q1:

Simplify the function 𝑛 ( π‘₯ ) = 1 π‘₯ + 3 βˆ’ 8 π‘₯ + 3 , and determine its domain.

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

Q2:

Simplify the function 𝑛 ( π‘₯ ) = 3 π‘₯ π‘₯ + 8 + 6 π‘₯ + 8 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 3 π‘₯ + 6 2 π‘₯ + 1 6 , domain = ℝ βˆ’ { βˆ’ 8 }
  • B 𝑛 ( π‘₯ ) = 3 ( π‘₯ + 2 ) π‘₯ + 8 , domain = ℝ βˆ’ { 8 }
  • C 𝑛 ( π‘₯ ) = 3 π‘₯ + 6 2 π‘₯ + 1 6 , domain = ℝ βˆ’ { 8 }
  • D 𝑛 ( π‘₯ ) = 3 ( π‘₯ + 2 ) π‘₯ + 8 , domain = ℝ βˆ’ { βˆ’ 8 }
  • E 𝑛 ( π‘₯ ) = 3 ( π‘₯ + 2 ) ( π‘₯ + 8 ) 2 , domain = ℝ βˆ’ { βˆ’ 8 }

Q3:

Simplify the function 𝑛 ( π‘₯ ) = 2 π‘₯ βˆ’ 8 + 4 8 βˆ’ π‘₯ , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 6 π‘₯ βˆ’ 8 , domain = ℝ βˆ’ { 8 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 2 π‘₯ βˆ’ 8 , domain = ℝ βˆ’ { βˆ’ 8 , 8 }
  • C 𝑛 ( π‘₯ ) = 6 π‘₯ βˆ’ 8 , domain = ℝ βˆ’ { βˆ’ 8 , 8 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 2 π‘₯ βˆ’ 8 , domain = ℝ βˆ’ { 8 }
  • E 𝑛 ( π‘₯ ) = 6 ( π‘₯ βˆ’ 8 ) ( 8 βˆ’ π‘₯ ) , domain = ℝ βˆ’ { 8 }

Q4:

Write as a single fraction in its simplest form.

  • A 3 6 1 6 π‘₯
  • B 9 8 π‘₯
  • C 3 6 π‘₯ 1 6 π‘₯ 2
  • D 9 4 π‘₯
  • E 1 2

Q5:

Simplify 3 π‘₯ + 2 π‘₯ + 3 + 3 π‘₯ π‘₯ + 3 2 2 2 .

  • A 3 π‘₯ + 3 π‘₯ + 2 2 ( π‘₯ + 3 ) 2 2
  • B 3 π‘₯ + 3 π‘₯ + 2 ( π‘₯ + 3 ) 2 2 2
  • C π‘₯ + π‘₯ + 2 ( π‘₯ + 2 ) 2 2 2
  • D 3 π‘₯ + 3 π‘₯ + 2 π‘₯ + 3 2 2
  • E 3 π‘₯ + 3 π‘₯ + 2 π‘₯ + 2 2 2

Q6:

Simplify the function 𝑛 ( π‘₯ ) = 8 π‘₯ βˆ’ 9 βˆ’ 4 π‘₯ βˆ’ 9 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ βˆ’ 9 , domain = ℝ βˆ’ { 9 }
  • B 𝑛 ( π‘₯ ) = 4 π‘₯ βˆ’ 9 , domain = ℝ βˆ’ { βˆ’ 9 }
  • C 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ βˆ’ 9 , domain = ℝ βˆ’ { βˆ’ 9 }
  • D 𝑛 ( π‘₯ ) = 4 π‘₯ βˆ’ 9 , domain = ℝ βˆ’ { 9 }
  • E 𝑛 ( π‘₯ ) = βˆ’ 2 9 , domain = ℝ βˆ’ { 9 }

Q7:

Simplify the function 𝑛 ( π‘₯ ) = 3 π‘₯ + 9 βˆ’ 9 π‘₯ + 9 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 6 π‘₯ + 9 , domain = ℝ βˆ’ { βˆ’ 9 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 6 π‘₯ + 9 , domain = ℝ βˆ’ { 9 }
  • C 𝑛 ( π‘₯ ) = 6 π‘₯ + 9 , domain = ℝ βˆ’ { 9 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 6 π‘₯ + 9 , domain = ℝ βˆ’ { βˆ’ 9 }
  • E 𝑛 ( π‘₯ ) = βˆ’ 1 3 , domain = ℝ βˆ’ { βˆ’ 9 }

Q8:

Simplify the function 𝑛 ( π‘₯ ) = 5 π‘₯ π‘₯ βˆ’ 9 + 9 π‘₯ βˆ’ 9 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 5 π‘₯ + 9 2 π‘₯ βˆ’ 1 8 , domain = ℝ βˆ’ { 9 }
  • B 𝑛 ( π‘₯ ) = 5 π‘₯ + 9 π‘₯ βˆ’ 9 , domain = ℝ βˆ’ { βˆ’ 9 }
  • C 𝑛 ( π‘₯ ) = 5 π‘₯ + 9 2 π‘₯ βˆ’ 1 8 , domain = ℝ βˆ’ { βˆ’ 9 }
  • D 𝑛 ( π‘₯ ) = 5 π‘₯ + 9 π‘₯ βˆ’ 9 , domain = ℝ βˆ’ { 9 }
  • E 𝑛 ( π‘₯ ) = 5 π‘₯ + 9 ( π‘₯ βˆ’ 9 ) 2 , domain = ℝ βˆ’ { 9 }

Q9:

Simplify the function 𝑛 ( π‘₯ ) = 8 π‘₯ βˆ’ 1 + 7 1 βˆ’ π‘₯ , and determine its domain.

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