Worksheet: Adding and Subtracting Rational Expressions with Like Denominators

In this worksheet, we will practice adding or subtracting two or more rational expressions with the same denominator.

Q1:

Simplify the function 𝑛 ( 𝑥 ) = 1 𝑥 + 3 8 𝑥 + 3 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 7 𝑥 + 3 , domain = { 3 }
  • B 𝑛 ( 𝑥 ) = 7 𝑥 + 3 , domain = { 3 }
  • C 𝑛 ( 𝑥 ) = 7 6 , domain = { 3 }
  • D 𝑛 ( 𝑥 ) = 7 𝑥 + 3 , domain = { 3 }
  • E 𝑛 ( 𝑥 ) = 7 𝑥 + 3 , domain = { 3 }

Q2:

Simplify the function 𝑛 ( 𝑥 ) = 3 𝑥 𝑥 + 8 + 6 𝑥 + 8 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 3 ( 𝑥 + 2 ) 𝑥 + 8 , domain = { 8 }
  • B 𝑛 ( 𝑥 ) = 3 𝑥 + 6 2 𝑥 + 1 6 , domain = { 8 }
  • C 𝑛 ( 𝑥 ) = 3 ( 𝑥 + 2 ) 𝑥 + 8 , domain = { 8 }
  • D 𝑛 ( 𝑥 ) = 3 𝑥 + 6 2 𝑥 + 1 6 , domain = { 8 }
  • E 𝑛 ( 𝑥 ) = 3 ( 𝑥 + 2 ) ( 𝑥 + 8 ) , domain = { 8 }

Q3:

Simplify the function 𝑛 ( 𝑥 ) = 2 𝑥 8 + 4 8 𝑥 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 6 𝑥 8 , domain = { 8 }
  • B 𝑛 ( 𝑥 ) = 2 𝑥 8 , domain = { 8 }
  • C 𝑛 ( 𝑥 ) = 6 ( 𝑥 8 ) ( 8 𝑥 ) , domain = { 8 }
  • D 𝑛 ( 𝑥 ) = 6 𝑥 8 , domain = { 8 , 8 }
  • E 𝑛 ( 𝑥 ) = 2 𝑥 8 , domain = { 8 , 8 }

Q4:

Write 3 4 𝑥 + 6 4 𝑥 as a single fraction in its simplest form.

  • A 3 6 𝑥 1 6 𝑥
  • B 3 6 1 6 𝑥
  • C 9 8 𝑥
  • D 9 4 𝑥
  • E 1 2

Q5:

Simplify 3 𝑥 + 2 𝑥 + 3 + 3 𝑥 𝑥 + 3 .

  • A 𝑥 + 𝑥 + 2 ( 𝑥 + 2 )
  • B 3 𝑥 + 3 𝑥 + 2 𝑥 + 3
  • C 3 𝑥 + 3 𝑥 + 2 ( 𝑥 + 3 )
  • D 3 𝑥 + 3 𝑥 + 2 𝑥 + 2
  • E 3 𝑥 + 3 𝑥 + 2 2 ( 𝑥 + 3 )

Q6:

Simplify the function 𝑛 ( 𝑥 ) = 3 𝑥 + 9 9 𝑥 + 9 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 6 𝑥 + 9 , domain = { 9 }
  • B 𝑛 ( 𝑥 ) = 6 𝑥 + 9 , domain = { 9 }
  • C 𝑛 ( 𝑥 ) = 1 3 , domain = { 9 }
  • D 𝑛 ( 𝑥 ) = 6 𝑥 + 9 , domain = { 9 }
  • E 𝑛 ( 𝑥 ) = 6 𝑥 + 9 , domain = { 9 }

Q7:

Simplify the function 𝑛 ( 𝑥 ) = 3 𝑥 + 6 7 𝑥 + 6 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 1 3 , domain = { 6 }
  • B 𝑛 ( 𝑥 ) = 4 𝑥 + 6 , domain = { 6 }
  • C 𝑛 ( 𝑥 ) = 4 𝑥 + 6 , domain = { 6 }
  • D 𝑛 ( 𝑥 ) = 4 𝑥 + 6 , domain = { 6 }
  • E 𝑛 ( 𝑥 ) = 4 𝑥 + 6 , domain = { 6 }

Q8:

Simplify the function 𝑛 ( 𝑥 ) = 9 𝑥 𝑥 + 3 + 8 𝑥 + 3 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 9 𝑥 + 8 2 𝑥 + 6 , domain = { 3 }
  • B 𝑛 ( 𝑥 ) = 9 𝑥 + 8 𝑥 + 3 , domain = { 3 }
  • C 𝑛 ( 𝑥 ) = 9 𝑥 + 8 ( 𝑥 + 3 ) , domain = { 3 }
  • D 𝑛 ( 𝑥 ) = 9 𝑥 + 8 𝑥 + 3 , domain = { 3 }
  • E 𝑛 ( 𝑥 ) = 9 𝑥 + 8 2 𝑥 + 6 , domain = { 3 }

Q9:

Simplify the function 𝑛 ( 𝑥 ) = 2 𝑥 6 + 4 6 𝑥 , and determine its domain.

  • A 𝑛 ( 𝑥 ) = 6 ( 𝑥 6 ) ( 6 𝑥 ) , domain = { 6 }
  • B 𝑛 ( 𝑥 ) = 2 𝑥 6 , domain = { 6 }
  • C 𝑛 ( 𝑥 ) = 6 𝑥 6 , domain = { 6 }
  • D 𝑛 ( 𝑥 ) = 2 𝑥 6 , domain = { 6 , 6 }
  • E 𝑛 ( 𝑥 ) = 6 𝑥 6 , domain = { 6 , 6 }

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.