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Worksheet: Adding and Subtracting Rational Expressions

Q1:

Simplify the function 𝑛 ( π‘₯ ) = βˆ’ 8 π‘₯ βˆ’ 6 + π‘₯ βˆ’ 6 π‘₯ βˆ’ 6 π‘₯ 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 1 4 π‘₯ ( π‘₯ βˆ’ 6 ) , domain = ℝ βˆ’ { 0 , 6 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 7 π‘₯ + 6 π‘₯ ( π‘₯ βˆ’ 6 ) , domain = ℝ βˆ’ { 0 , βˆ’ 6 }
  • C 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 1 4 π‘₯ ( π‘₯ βˆ’ 6 ) , domain = ℝ βˆ’ { 0 , βˆ’ 6 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 7 π‘₯ + 6 π‘₯ ( π‘₯ βˆ’ 6 ) , domain = ℝ βˆ’ { 0 , 6 }
  • E 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 1 4 π‘₯ βˆ’ 5 π‘₯ βˆ’ 6 2 , domain = ℝ βˆ’ { 0 , 6 }

Q2:

Simplify the function 𝑛 ( π‘₯ ) = 3 π‘₯ π‘₯ + 4 βˆ’ 7 π‘₯ π‘₯ βˆ’ 4 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) , domain = ℝ βˆ’ { βˆ’ 4 , 4 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ ( π‘₯ + 1 0 ) ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) , domain = { βˆ’ 4 , 4 }
  • C 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) , domain = { βˆ’ 4 , 4 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ ( π‘₯ + 1 0 ) ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) , domain = ℝ βˆ’ { βˆ’ 4 , 4 }
  • E 𝑛 ( π‘₯ ) = βˆ’ 4 π‘₯ ( π‘₯ βˆ’ 1 0 ) ( π‘₯ + 4 ) ( π‘₯ βˆ’ 4 ) , domain = { βˆ’ 4 , 4 }

Q3:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 7 π‘₯ βˆ’ 3 π‘₯ βˆ’ 2 8 βˆ’ π‘₯ βˆ’ 7 7 βˆ’ π‘₯ 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = π‘₯ + 5 π‘₯ βˆ’ 4 , domain = ℝ βˆ’ { 4 , 7 }
  • B 𝑛 ( π‘₯ ) = π‘₯ + 5 π‘₯ + 4 , domain = ℝ βˆ’ { βˆ’ 4 }
  • C 𝑛 ( π‘₯ ) = π‘₯ + 5 π‘₯ βˆ’ 4 , domain = ℝ βˆ’ { 4 }
  • D 𝑛 ( π‘₯ ) = π‘₯ + 5 π‘₯ + 4 , domain = ℝ βˆ’ { βˆ’ 4 , 7 }
  • E 𝑛 ( π‘₯ ) = 2 π‘₯ + 4 , domain = ℝ βˆ’ { βˆ’ 4 , 7 }

Q4:

Answer the following questions for the rational expressions π‘₯ + 3 3 and π‘₯ βˆ’ 8 2 π‘₯ .

Find the sum of π‘₯ + 3 3 and π‘₯ βˆ’ 8 2 π‘₯ .

  • A π‘₯ + 9 π‘₯ βˆ’ 2 4 6 π‘₯ 
  • B 2 π‘₯ + 3 π‘₯ + 5 π‘₯ 
  • C 2 π‘₯ + 3 π‘₯ βˆ’ 5 π‘₯ 
  • D 2 π‘₯ + 9 π‘₯ βˆ’ 2 4 6 π‘₯ 
  • E π‘₯ + 9 π‘₯ βˆ’ 2 4 6 π‘₯ 

Is the sum of π‘₯ + 3 3 and π‘₯ βˆ’ 8 2 π‘₯ a rational expression?

  • A yes
  • B no

Would this be true for any two rational expressions summed together?

  • A no
  • B yes

Q5:

Simplify the function 𝑛 ( π‘₯ ) = 7 π‘₯ π‘₯ βˆ’ 1 + 3 π‘₯ 1 βˆ’ π‘₯ 2 , and determine its domain.

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

Q6:

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

  • A 𝑛 ( π‘₯ ) = 4 π‘₯ + 1 3 3 π‘₯ , domain = ℝ βˆ’ { 0 }
  • B 𝑛 ( π‘₯ ) = 4 π‘₯ + 2 7 3 π‘₯ , domain = ℝ βˆ’ { 0 , 3 }
  • C 𝑛 ( π‘₯ ) = 4 π‘₯ + 1 3 3 π‘₯ , domain = ℝ βˆ’ { 0 , 3 }
  • D 𝑛 ( π‘₯ ) = 4 π‘₯ + 2 7 3 π‘₯ , domain = ℝ βˆ’ { 0 }
  • E 𝑛 ( π‘₯ ) = 2 π‘₯ + 1 3 4 π‘₯ , domain = ℝ βˆ’ { 0 }

Q7:

Given that the domain of the function 𝑛 ( π‘₯ ) = 𝑏 π‘₯ + 6 π‘₯ + π‘Ž is ℝ βˆ’ { βˆ’ 4 , 0 } , and 𝑛 ( βˆ’ 1 ) = 2 , find the values of π‘Ž and 𝑏 .

  • A π‘Ž = 4 , 𝑏 = 2
  • B π‘Ž = βˆ’ 4 , 𝑏 = 0
  • C π‘Ž = βˆ’ 4 , 𝑏 = 2
  • D π‘Ž = 4 , 𝑏 = 0
  • E π‘Ž = 4 , 𝑏 = βˆ’ 4

Q8:

Simplify the function 𝑛 ( π‘₯ ) = ο€Ό 4 π‘₯ βˆ’ 8 π‘₯ + 2 π‘₯ βˆ’ 8 + 2 π‘₯ + 4 π‘₯ + 4  Γ— π‘₯ + 2 7 π‘₯ βˆ’ 3 π‘₯ + 9 2 3 2 , and find its domain.

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

Q9:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ + 3 π‘₯ βˆ’ 4 9 βˆ’ 3 π‘₯ + 2 1 π‘₯ 3 π‘₯ βˆ’ 6 π‘₯ βˆ’ 1 0 5 π‘₯ 2 3 2 4 3 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 2 ( 1 1 π‘₯ + 3 2 ) ( π‘₯ βˆ’ 7 ) ( π‘₯ + 7 ) ( π‘₯ + 5 ) , domain = ℝ βˆ’ { βˆ’ 7 , βˆ’ 5 , 0 , 7 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 2 ( 3 π‘₯ + 1 7 ) ( π‘₯ βˆ’ 7 ) ( π‘₯ + 7 ) ( π‘₯ + 5 ) , domain = ℝ βˆ’ { βˆ’ 7 , βˆ’ 5 , 7 }
  • C 𝑛 ( π‘₯ ) = 2 ( 1 1 π‘₯ + 3 2 ) ( π‘₯ βˆ’ 7 ) ( π‘₯ + 7 ) ( π‘₯ + 5 ) , domain = ℝ βˆ’ { βˆ’ 7 , βˆ’ 5 , 7 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 2 ( 3 π‘₯ + 1 7 ) ( π‘₯ βˆ’ 7 ) ( π‘₯ + 7 ) ( π‘₯ + 5 ) , domain = ℝ βˆ’ { βˆ’ 7 , βˆ’ 5 , 0 , 7 }
  • E 𝑛 ( π‘₯ ) = βˆ’ 3 π‘₯ βˆ’ 2 1 π‘₯ + π‘₯ + 3 ( π‘₯ βˆ’ 7 ) ( π‘₯ + 7 ) ( π‘₯ + 5 ) 3 2 , domain = ℝ βˆ’ { βˆ’ 7 , βˆ’ 5 , 0 , 7 }

Q10:

Simplify the function 𝑛 ( π‘₯ ) = 8 π‘₯ + 7 π‘₯ βˆ’ 1 4 π‘₯ + 4 5 + 3 π‘₯ βˆ’ 2 4 π‘₯ βˆ’ 1 7 π‘₯ + 7 2 2 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 1 1 π‘₯ βˆ’ 1 7 2 π‘₯ βˆ’ 3 1 π‘₯ + 1 1 7 2 , domain = ℝ βˆ’ { 5 , 8 , 9 }
  • B 𝑛 ( π‘₯ ) = 1 1 π‘₯ βˆ’ 8 ( π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 5 ) , domain = ℝ βˆ’ { 5 , 9 }
  • C 𝑛 ( π‘₯ ) = 2 ( 4 π‘₯ + 5 ) ( π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 5 ) , domain = ℝ βˆ’ { 5 , 8 , 9 }
  • D 𝑛 ( π‘₯ ) = 1 1 π‘₯ βˆ’ 8 ( π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 5 ) , domain = ℝ βˆ’ { 5 , 8 , 9 }
  • E 𝑛 ( π‘₯ ) = 2 ( 4 π‘₯ + 5 ) ( π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 5 ) , domain = ℝ βˆ’ { 5 , 9 }

Q11:

Simplify the function 𝑛 ( π‘₯ ) = 6 4 π‘₯ βˆ’ 1 + 9 9 π‘₯ βˆ’ 1 8 π‘₯ 2 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 1 5 βˆ’ 1 4 π‘₯ + 9 π‘₯ βˆ’ 1 2 , domain = ℝ βˆ’  βˆ’ 1 2 , 0 , 1 2 
  • B 𝑛 ( π‘₯ ) = 4 π‘₯ βˆ’ 1 π‘₯ ( 2 π‘₯ + 1 ) ( 2 π‘₯ βˆ’ 1 ) , domain = ℝ βˆ’  βˆ’ 1 2 , 1 2 
  • C 𝑛 ( π‘₯ ) = 5 π‘₯ ( 2 π‘₯ + 1 ) ( 2 π‘₯ βˆ’ 1 ) , domain = ℝ βˆ’  βˆ’ 1 2 , 0 , 1 2 
  • D 𝑛 ( π‘₯ ) = 4 π‘₯ βˆ’ 1 π‘₯ ( 2 π‘₯ + 1 ) ( 2 π‘₯ βˆ’ 1 ) , domain = ℝ βˆ’  βˆ’ 1 2 , 0 , 1 2 

Q12:

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

  • A 𝑛 ( π‘₯ ) = 1 8 , domain = ℝ βˆ’  0 , 8 3 
  • B 𝑛 ( π‘₯ ) = βˆ’ 5 π‘₯ + 8 3 π‘₯ ( 3 π‘₯ βˆ’ 8 ) , domain = ℝ βˆ’  0 , βˆ’ 8 3 
  • C 𝑛 ( π‘₯ ) = 1 8 , domain = ℝ
  • D 𝑛 ( π‘₯ ) = βˆ’ 5 π‘₯ + 8 3 π‘₯ ( 3 π‘₯ βˆ’ 8 ) , domain = ℝ βˆ’  0 , 8 3 

Q13:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ + π‘₯ + 1 π‘₯ βˆ’ 1 βˆ’ 8 1 βˆ’ π‘₯ π‘₯ βˆ’ 1 0 π‘₯ + 9 2 3 2 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 8 π‘₯ βˆ’ 1 , domain = ℝ βˆ’ { 1 , 9 }
  • B 𝑛 ( π‘₯ ) = π‘₯ + 1 0 π‘₯ βˆ’ 1 , domain = ℝ βˆ’ { 1 }
  • C 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 8 π‘₯ βˆ’ 1 , domain = ℝ βˆ’ { 1 }
  • D 𝑛 ( π‘₯ ) = π‘₯ + 1 0 π‘₯ βˆ’ 1 , domain = ℝ βˆ’ { 1 , 9 }
  • E 𝑛 ( π‘₯ ) = βˆ’ π‘₯ βˆ’ 8 π‘₯ βˆ’ 1 , domain = ℝ βˆ’ { 1 , 9 }

Q14:

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

  • A 𝑛 ( π‘₯ ) = 6 4 π‘₯ + 8 , domain = ℝ βˆ’ { βˆ’ 8 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 6 4 π‘₯ + 8 , domain = ℝ βˆ’ { 8 }
  • C 𝑛 ( π‘₯ ) = βˆ’ π‘₯ + π‘₯ βˆ’ 8 π‘₯ + 8 2 , domain = ℝ βˆ’ { βˆ’ 8 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 6 4 π‘₯ + 8 , domain = ℝ βˆ’ { βˆ’ 8 }
  • E 𝑛 ( π‘₯ ) = 6 4 π‘₯ + 8 , domain = ℝ βˆ’ { 8 }

Q15:

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

  • A 𝑛 ( π‘₯ ) = 1 8 ( π‘₯ βˆ’ 6 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’ { βˆ’ 6 , 6 }
  • B 𝑛 ( π‘₯ ) = 1 8 π‘₯ ( π‘₯ βˆ’ 6 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’ { 6 }
  • C 𝑛 ( π‘₯ ) = 9 π‘₯ , domain = ℝ βˆ’ { βˆ’ 6 , 6 }
  • D 𝑛 ( π‘₯ ) = 1 8 π‘₯ ( π‘₯ βˆ’ 6 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’ { βˆ’ 6 , 6 }

Q16:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 6 8 π‘₯ βˆ’ 5 7 π‘₯ + 5 4 + π‘₯ βˆ’ 5 8 1 π‘₯ βˆ’ 8 1 βˆ’ 8 π‘₯ 2 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = βˆ’ 1 4 ( 8 π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 9 ) , domain = ℝ βˆ’  9 8 , 6 , 9 
  • B 𝑛 ( π‘₯ ) = βˆ’ 4 ( 8 π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 9 ) , domain = ℝ βˆ’  9 8 , 9 
  • C 𝑛 ( π‘₯ ) = βˆ’ 1 4 ( 8 π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 9 ) , domain = ℝ βˆ’  9 8 , 9 
  • D 𝑛 ( π‘₯ ) = βˆ’ 4 ( 8 π‘₯ βˆ’ 9 ) ( π‘₯ βˆ’ 9 ) , domain = ℝ βˆ’  9 8 , 6 , 9 
  • E 𝑛 ( π‘₯ ) = 1 4 ( 8 π‘₯ + 9 ) ( π‘₯ + 9 ) , domain = ℝ βˆ’  βˆ’ 9 8 , βˆ’ 6 , βˆ’ 9 

Q17:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ + 7 5 π‘₯ + 3 9 π‘₯ + 2 8 + π‘₯ + 4 βˆ’ 3 4 π‘₯ βˆ’ 2 4 βˆ’ 5 π‘₯ 2 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 1 0 ( 5 π‘₯ + 4 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’  βˆ’ 4 5 , βˆ’ 7 , βˆ’ 6 
  • B 𝑛 ( π‘₯ ) = 2 ( 5 π‘₯ + 4 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’  βˆ’ 4 5 , βˆ’ 6 
  • C 𝑛 ( π‘₯ ) = 1 0 ( 5 π‘₯ + 4 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’  βˆ’ 4 5 , βˆ’ 6 
  • D 𝑛 ( π‘₯ ) = 2 ( 5 π‘₯ + 4 ) ( π‘₯ + 6 ) , domain = ℝ βˆ’  βˆ’ 4 5 , βˆ’ 7 , βˆ’ 6 
  • E 𝑛 ( π‘₯ ) = βˆ’ 1 0 ( 5 π‘₯ βˆ’ 4 ) ( π‘₯ βˆ’ 6 ) , domain = ℝ βˆ’  4 5 , 7 , 6 

Q18:

Answer the following questions for the rational expressions 5 π‘₯ βˆ’ 2 3 π‘₯ and 3 π‘₯ βˆ’ 2 π‘₯ 2 π‘₯ + 8  .

Subtract 5 π‘₯ βˆ’ 2 3 π‘₯ from 3 π‘₯ βˆ’ 2 π‘₯ 2 π‘₯ + 8  .

  • A π‘₯ βˆ’ 3 π‘₯ + 3 6 π‘₯ π‘₯ ( π‘₯ + 4 )  
  • B π‘₯ + 2 π‘₯ βˆ’ 3 6 π‘₯ + 1 6 6 π‘₯ ( π‘₯ + 4 )  
  • C 9 π‘₯ βˆ’ 2 π‘₯ βˆ’ 3 6 π‘₯ + 1 6 6 π‘₯ ( π‘₯ + 4 )  
  • D 9 π‘₯ βˆ’ 1 6 π‘₯ βˆ’ 3 6 π‘₯ + 1 6 6 π‘₯ ( π‘₯ + 4 )  
  • E π‘₯ βˆ’ 1 6 π‘₯ + 3 6 π‘₯ π‘₯ ( π‘₯ + 4 )  

Is the difference between 3 π‘₯ βˆ’ 2 π‘₯ 2 π‘₯ + 8  and 5 π‘₯ βˆ’ 2 3 π‘₯ a rational expression?

  • A yes
  • B no

Is the result of this subtraction a rational expression?

  • A no
  • B yes

Q19:

Simplify the function 𝑛 ( π‘₯ ) = 5 π‘₯ π‘₯ βˆ’ 4 βˆ’ π‘₯ + 4 π‘₯ βˆ’ 1 6 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 5 π‘₯ + 1 π‘₯ βˆ’ 4 , domain = ℝ βˆ’ { βˆ’ 4 , 4 }
  • B 𝑛 ( π‘₯ ) = 5 π‘₯ βˆ’ 1 π‘₯ βˆ’ 4 , domain = ℝ βˆ’ { 4 }
  • C 𝑛 ( π‘₯ ) = 5 π‘₯ + 1 π‘₯ βˆ’ 4 , domain = ℝ βˆ’ { 4 }
  • D 𝑛 ( π‘₯ ) = 5 π‘₯ βˆ’ 1 π‘₯ βˆ’ 4 , domain = ℝ βˆ’ { βˆ’ 4 , 4 }
  • E 𝑛 ( π‘₯ ) = 4 ( π‘₯ βˆ’ 1 ) ( π‘₯ βˆ’ 4 ) ( π‘₯ βˆ’ 1 6 ) 2 , domain = ℝ βˆ’ { βˆ’ 4 , 4 }

Q20:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 7 6 π‘₯ βˆ’ 3 5 π‘₯ βˆ’ 4 9 + π‘₯ + 2 1 4 + 1 9 π‘₯ + 6 π‘₯ 2 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = 2 6 π‘₯ βˆ’ 7 , domain = ℝ βˆ’  7 , βˆ’ 2 , βˆ’ 7 6 
  • B 𝑛 ( π‘₯ ) = 2 6 π‘₯ + 7 , domain = ℝ βˆ’  βˆ’ 7 6 
  • C 𝑛 ( π‘₯ ) = 2 6 π‘₯ βˆ’ 7 , domain = ℝ βˆ’  7 6 
  • D 𝑛 ( π‘₯ ) = 2 6 π‘₯ + 7 , domain = ℝ βˆ’  7 , βˆ’ 2 , βˆ’ 7 6 
  • E 𝑛 ( π‘₯ ) = 2 π‘₯ βˆ’ 5 1 2 π‘₯ βˆ’ 1 6 π‘₯ βˆ’ 3 5 2 , domain = ℝ βˆ’  7 , βˆ’ 2 , βˆ’ 7 6 

Q21:

Simplify the function 𝑛 ( π‘₯ ) = π‘₯ βˆ’ 4 π‘₯ βˆ’ 3 2 π‘₯ βˆ’ 1 6 π‘₯ + 6 4 + π‘₯ βˆ’ 8 π‘₯ + 1 2 π‘₯ βˆ’ 1 0 π‘₯ + 1 6 2 2 2 2 , and determine its domain.

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

Q22:

Simplify the function 𝑛 ( π‘₯ ) = βˆ’ 5 π‘₯ + 8 + 7 π‘₯ + 4 6 4 βˆ’ π‘₯ 2 , and determine its domain.

  • A 𝑛 ( π‘₯ ) = βˆ’ 4 ( 3 π‘₯ + 1 1 ) ( π‘₯ βˆ’ 8 ) ( π‘₯ + 8 ) , domain = ℝ βˆ’ { βˆ’ 8 , 8 }
  • B 𝑛 ( π‘₯ ) = βˆ’ 1 2 ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 8 ) ( π‘₯ + 8 ) , domain = ℝ βˆ’ { βˆ’ 8 }
  • C 𝑛 ( π‘₯ ) = βˆ’ 4 ( 3 π‘₯ + 1 1 ) ( π‘₯ βˆ’ 8 ) ( π‘₯ + 8 ) , domain = ℝ βˆ’ { βˆ’ 8 }
  • D 𝑛 ( π‘₯ ) = βˆ’ 1 2 ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 8 ) ( π‘₯ + 8 ) , domain = ℝ βˆ’ { βˆ’ 8 , 8 }
  • E 𝑛 ( π‘₯ ) = βˆ’ 1 2 ( π‘₯ + 3 ) ( π‘₯ βˆ’ 8 ) ( π‘₯ + 8 ) , domain = ℝ βˆ’ { βˆ’ 8 , 8 }

Q23:

Given that the domain of the function 𝑛 ( π‘₯ ) = 2 π‘₯ ( π‘₯ βˆ’ π‘Ž ) ( π‘₯ + 6 ) + 5 π‘₯ + 5 ( π‘₯ βˆ’ π‘Ž ) ( π‘₯ + 3 ) is ℝ βˆ’ { βˆ’ 6 , βˆ’ 3 , 2 } , what is the value of π‘Ž ?

  • A { βˆ’ 2 }
  • B ℝ βˆ’ { 2 }
  • C ℝ βˆ’ { βˆ’ 2 }
  • D { 2 }
  • E ℝ βˆ’ { βˆ’ 6 , βˆ’ 3 , 2 }